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Volumn 12, Issue C, 2005, Pages 393-514

Semidefinite Programming and Integer Programming

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EID: 33745858905     PISSN: 09270507     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0927-0507(05)12008-8     Document Type: Review
Times cited : (113)

References (245)
  • 1
    • 0242271908 scopus 로고    scopus 로고
    • Lift and project relaxations for the matching polytope and related polytopes
    • Aguilera N.E., Bianchi S.M., and Nasini G.L. Lift and project relaxations for the matching polytope and related polytopes. Discrete Applied Mathematics 134 (2004) 193-212
    • (2004) Discrete Applied Mathematics , vol.134 , pp. 193-212
    • Aguilera, N.E.1    Bianchi, S.M.2    Nasini, G.L.3
  • 4
    • 0034395202 scopus 로고    scopus 로고
    • Graph rigidity via Euclidean distance matrices
    • Alfakih A. Graph rigidity via Euclidean distance matrices. Linear Algebra and its Applications 310 (2000) 149-165
    • (2000) Linear Algebra and its Applications , vol.310 , pp. 149-165
    • Alfakih, A.1
  • 5
    • 0035606028 scopus 로고    scopus 로고
    • On rigidity and realizability of weighted graphs
    • Alfakih A. On rigidity and realizability of weighted graphs. Linear Algebra and its Applications 325 (2001) 57-70
    • (2001) Linear Algebra and its Applications , vol.325 , pp. 57-70
    • Alfakih, A.1
  • 8
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications in combinatorial optimization
    • Alizadeh F. Interior point methods in semidefinite programming with applications in combinatorial optimization. SIAM Journal on Optimization 5 (1995) 13-51
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 9
    • 0001262835 scopus 로고    scopus 로고
    • Approximating the independence number via the θ{symbol}-function
    • Alon N., and Kahale N. Approximating the independence number via the θ{symbol}-function. Mathematical Programming 80 (1998) 253-264
    • (1998) Mathematical Programming , vol.80 , pp. 253-264
    • Alon, N.1    Kahale, N.2
  • 11
    • 10844234989 scopus 로고    scopus 로고
    • Constructing worst case instances for semidefinite programming based approximation algorithms
    • [Preliminary version in Proceedings of 12 th ACM-SIAM Symposium on Discrete Algorithms, pages 92-100, 2001.]
    • Alon N., Sudakov B., and Zwick U. Constructing worst case instances for semidefinite programming based approximation algorithms. SIAM Journal on Discrete Mathematics 15 (2002) 58-72 [Preliminary version in Proceedings of 12 th ACM-SIAM Symposium on Discrete Algorithms, pages 92-100, 2001.]
    • (2002) SIAM Journal on Discrete Mathematics , vol.15 , pp. 58-72
    • Alon, N.1    Sudakov, B.2    Zwick, U.3
  • 13
    • 77950473896 scopus 로고    scopus 로고
    • An improved semidefinite programming relaxation for the satisfiability problem
    • Anjos M. An improved semidefinite programming relaxation for the satisfiability problem. Mathematical Programming (2004)
    • (2004) Mathematical Programming
    • Anjos, M.1
  • 14
    • 84867947404 scopus 로고    scopus 로고
    • Strengthened semidefinite relaxations via a second lifting for the max-cut problem
    • Anjos M.F., and Wolkowicz H. Strengthened semidefinite relaxations via a second lifting for the max-cut problem. Discrete Applied Mathematics 119 (2002) 79-106
    • (2002) Discrete Applied Mathematics , vol.119 , pp. 79-106
    • Anjos, M.F.1    Wolkowicz, H.2
  • 16
    • 0000990727 scopus 로고    scopus 로고
    • A lower bound for the Quadratic Assignment Problem based on Convex Quadratic Programming
    • Anstreicher K., and Brixius N. A lower bound for the Quadratic Assignment Problem based on Convex Quadratic Programming. Mathematical Programming 89 (2001) 341-357
    • (2001) Mathematical Programming , vol.89 , pp. 341-357
    • Anstreicher, K.1    Brixius, N.2
  • 24
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • Balas E., Ceria S., and Cornuéjols G. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58 (1993) 295-324
    • (1993) Mathematical Programming , vol.58 , pp. 295-324
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 26
    • 0027610254 scopus 로고
    • On cuts and matchings in planar graphs
    • Barahona F. On cuts and matchings in planar graphs. Mathematical Programming 60 (1993) 53-68
    • (1993) Mathematical Programming , vol.60 , pp. 53-68
    • Barahona, F.1
  • 27
    • 0001051761 scopus 로고
    • On the computational complexity of Ising spin glass models
    • Barahona F. On the computational complexity of Ising spin glass models. Journal of Physics A, Mathematical and General 15 (1982) 3241-3253
    • (1982) Journal of Physics A, Mathematical and General , vol.15 , pp. 3241-3253
    • Barahona, F.1
  • 31
    • 51249169354 scopus 로고
    • Feasibility testing for systems of real quadratic equations
    • Barvinok A.I. Feasibility testing for systems of real quadratic equations. Discrete and Computational Geometry 10 (1993) 1-13
    • (1993) Discrete and Computational Geometry , vol.10 , pp. 1-13
    • Barvinok, A.I.1
  • 32
    • 51249170448 scopus 로고
    • Problems of distance geometry and convex properties of quadratic maps
    • Barvinok A.I. Problems of distance geometry and convex properties of quadratic maps. Discrete and Computational Geometry 13 (1995) 189-202
    • (1995) Discrete and Computational Geometry , vol.13 , pp. 189-202
    • Barvinok, A.I.1
  • 33
    • 0035584604 scopus 로고    scopus 로고
    • A remark on the rank of positive semidefinite matrices subject to affine constraints
    • Barvinok A.I. A remark on the rank of positive semidefinite matrices subject to affine constraints. Discrete and Computational Geometry 25 (2001) 23-31
    • (2001) Discrete and Computational Geometry , vol.25 , pp. 23-31
    • Barvinok, A.I.1
  • 35
    • 58149362273 scopus 로고
    • The complexity of approximating a nonlinear program
    • Bellare M., and Rogaway P. The complexity of approximating a nonlinear program. Mathematical programming 69 (1995) 429-441
    • (1995) Mathematical programming , vol.69 , pp. 429-441
    • Bellare, M.1    Rogaway, P.2
  • 38
    • 14944344548 scopus 로고    scopus 로고
    • Subset algebra lift operators for 0 - 1 integer programming
    • Bienstock D., and Zuckerberg M. Subset algebra lift operators for 0 - 1 integer programming. SIAM Journal on Optimization 15 (2004) 63-95
    • (2004) SIAM Journal on Optimization , vol.15 , pp. 63-95
    • Bienstock, D.1    Zuckerberg, M.2
  • 39
    • 0028425392 scopus 로고
    • New approximation algorithms for graph coloring
    • [Preliminary version in Proceedings of the 21st Annual ACM Symposium on Theory of Computing, ACM, New York, pages 535-542, 1989 and in Proceedings of the 31st IEEE Symposium on Foundations of Computer Science, IEEE Computer Science Press, Los Alamitos, CA, pages 554-562, 1990.]
    • Blum A. New approximation algorithms for graph coloring. Journal of the Association for Computing Machinery 41 (1994) 470-516 [Preliminary version in Proceedings of the 21st Annual ACM Symposium on Theory of Computing, ACM, New York, pages 535-542, 1989 and in Proceedings of the 31st IEEE Symposium on Foundations of Computer Science, IEEE Computer Science Press, Los Alamitos, CA, pages 554-562, 1990.]
    • (1994) Journal of the Association for Computing Machinery , vol.41 , pp. 470-516
    • Blum, A.1
  • 44
    • 31244435061 scopus 로고    scopus 로고
    • Solving standard quadratic optimization problems via linear, semidefinite and copositive programming
    • Bomze I.M., and de Klerk E. Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. Journal of Global Optimization 24 (2002) 163-185
    • (2002) Journal of Global Optimization , vol.24 , pp. 163-185
    • Bomze, I.M.1    de Klerk, E.2
  • 46
    • 51249178997 scopus 로고
    • On Lipschitz embedding of finite metric spaces in Hilbert space
    • Bourgain J. On Lipschitz embedding of finite metric spaces in Hilbert space. Israel Journal of Mathematics 52 (1985) 46-52
    • (1985) Israel Journal of Mathematics , vol.52 , pp. 46-52
    • Bourgain, J.1
  • 47
    • 24944511808 scopus 로고    scopus 로고
    • On the separation of split cuts and related inequalities
    • Caprara A., and Letchford A.N. On the separation of split cuts and related inequalities. Mathematical Programming Series B 94 (2003) 279-294
    • (2003) Mathematical Programming Series B , vol.94 , pp. 279-294
    • Caprara, A.1    Letchford, A.N.2
  • 50
    • 84958754907 scopus 로고    scopus 로고
    • Solving integer and disjunctive programs by lift-and-project
    • Bixby R.E., Boyd E.A., and Rios-Mercato R.Z. (Eds)
    • Ceria S., and Pataki G. Solving integer and disjunctive programs by lift-and-project. In: Bixby R.E., Boyd E.A., and Rios-Mercato R.Z. (Eds). IPCO VI, Lecture Notes in Computer Science 1412 (1998) 271-283
    • (1998) IPCO VI, Lecture Notes in Computer Science , vol.1412 , pp. 271-283
    • Ceria, S.1    Pataki, G.2
  • 53
    • 0000971541 scopus 로고
    • Edmonds polytopes and a hierarchy of combinatorial problems
    • Chvátal V. Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Mathematics 4 (1973) 305-337
    • (1973) Discrete Mathematics , vol.4 , pp. 305-337
    • Chvátal, V.1
  • 54
    • 0002716241 scopus 로고
    • On certain polytopes associated with graphs
    • Chvátal V. On certain polytopes associated with graphs. Journal of Combinatorial Theroy B 18 (1975) 138-154
    • (1975) Journal of Combinatorial Theroy B , vol.18 , pp. 138-154
    • Chvátal, V.1
  • 57
    • 0025446910 scopus 로고
    • Chvátal closures for mixed integer programming problems
    • Cook W., Kannan R., and Schrijver A. Chvátal closures for mixed integer programming problems. Mathematical Programming 47 (1990) 155-174
    • (1990) Mathematical Programming , vol.47 , pp. 155-174
    • Cook, W.1    Kannan, R.2    Schrijver, A.3
  • 59
    • 26344442759 scopus 로고    scopus 로고
    • On the rank of mixed 0-1 polyhedra
    • Aardal K., and Gerards A.M.H. (Eds)
    • Cornuéjols G., and Li Y. On the rank of mixed 0-1 polyhedra. In: Aardal K., and Gerards A.M.H. (Eds). IPCO 2001, Lecture Notes in Computer Science 2081 (2001) 71-77
    • (2001) IPCO 2001, Lecture Notes in Computer Science , vol.2081 , pp. 71-77
    • Cornuéjols, G.1    Li, Y.2
  • 60
    • 27744594647 scopus 로고    scopus 로고
    • A connection between cutting plane theory and the geometry of numbers
    • Cornuéjols G., and Li Y. A connection between cutting plane theory and the geometry of numbers. Mathematical Programming A 93 (2002) 123-127
    • (2002) Mathematical Programming A , vol.93 , pp. 123-127
    • Cornuéjols, G.1    Li, Y.2
  • 64
    • 77950506014 scopus 로고    scopus 로고
    • An exponential lower bound on the length of some classes of branch-and-cut proofs
    • Cook W.J., and Schulz A.S. (Eds)
    • Dash S. An exponential lower bound on the length of some classes of branch-and-cut proofs. In: Cook W.J., and Schulz A.S. (Eds). IPCO 2002, Lecture Notes in Computer Science 2337 (2002) 145-160
    • (2002) IPCO 2002, Lecture Notes in Computer Science , vol.2337 , pp. 145-160
    • Dash, S.1
  • 65
    • 34250080270 scopus 로고
    • Laplacian eigenvalues and the maximum cut problem
    • Delorme C., and Poljak S. Laplacian eigenvalues and the maximum cut problem. Mathematical Programming 62 (1993) 557-574
    • (1993) Mathematical Programming , vol.62 , pp. 557-574
    • Delorme, C.1    Poljak, S.2
  • 66
    • 38249002036 scopus 로고
    • Combinatorial properties and the complexity of a max-cut approximation
    • Delorme C., and Poljak S. Combinatorial properties and the complexity of a max-cut approximation. European Journal of Combinatorics 14 (1993) 313-333
    • (1993) European Journal of Combinatorics , vol.14 , pp. 313-333
    • Delorme, C.1    Poljak, S.2
  • 67
    • 0010903176 scopus 로고
    • The performance of an eigenvalue bound on the max-cut problem in some classes of graphs
    • Delorme C., and Poljak S. The performance of an eigenvalue bound on the max-cut problem in some classes of graphs. Discrete Mathematics 111 (1993) 145-156
    • (1993) Discrete Mathematics , vol.111 , pp. 145-156
    • Delorme, C.1    Poljak, S.2
  • 68
    • 85041979556 scopus 로고
    • An algebraic approach to the association schemes of coding theory
    • Delsarte P. An algebraic approach to the association schemes of coding theory. Philips Research Reports Supplements No. 10 (1973)
    • (1973) Philips Research Reports Supplements , Issue.10
    • Delsarte, P.1
  • 73
    • 77950476892 scopus 로고    scopus 로고
    • The semidefinite relaxation of the k-partition polytope is strong
    • Cook W.J., and Schulz A.S. (Eds)
    • Eisenblätter A. The semidefinite relaxation of the k-partition polytope is strong. In: Cook W.J., and Schulz A.S. (Eds). IPCO 2002, Lecture Notes in Computer Science 2337 (2002) 273-290
    • (2002) IPCO 2002, Lecture Notes in Computer Science , vol.2337 , pp. 273-290
    • Eisenblätter, A.1
  • 74
    • 0039522018 scopus 로고    scopus 로고
    • On the membership problem for the elementary closure of a polyhedron
    • Eisenbrand F. On the membership problem for the elementary closure of a polyhedron. Combinatorica 19 (1999) 299-300
    • (1999) Combinatorica , vol.19 , pp. 299-300
    • Eisenbrand, F.1
  • 75
    • 84948952840 scopus 로고    scopus 로고
    • Bounds on the Chvátal rank of polytopes in the 0/1 cube
    • Cornuéjols G., et al. (Ed)
    • Eisenbrand F., and Schulz A.S. Bounds on the Chvátal rank of polytopes in the 0/1 cube. In: Cornuéjols G., et al. (Ed). IPCO 1999, Lecture Notes in Computer Science 1610 (1999) 137-150
    • (1999) IPCO 1999, Lecture Notes in Computer Science , vol.1610 , pp. 137-150
    • Eisenbrand, F.1    Schulz, A.S.2
  • 76
    • 0031474843 scopus 로고    scopus 로고
    • Randomized graph products, chromatic numbers, and the Lovász θ{symbol}-function
    • [Preliminary version in Proceedings of the 27th Annual ACM Symposium on Theory of Computing, ACM, New York, pp. 635-640, 1995.]
    • Feige U. Randomized graph products, chromatic numbers, and the Lovász θ{symbol}-function. Combinatorica 17 (1997) 79-90 [Preliminary version in Proceedings of the 27th Annual ACM Symposium on Theory of Computing, ACM, New York, pp. 635-640, 1995.]
    • (1997) Combinatorica , vol.17 , pp. 79-90
    • Feige, U.1
  • 77
    • 22644450239 scopus 로고    scopus 로고
    • Randomized rounding of semidefinite programs - variations on the MAX CUT example. Randomization, Approximation, and Combinatorial Optimization, Proceedings of Random-Approx'99
    • Springer-Verlag
    • Feige U. Randomized rounding of semidefinite programs - variations on the MAX CUT example. Randomization, Approximation, and Combinatorial Optimization, Proceedings of Random-Approx'99. Lecture Notes in Computer Science 1671 (1999) 189-196 Springer-Verlag
    • (1999) Lecture Notes in Computer Science , vol.1671 , pp. 189-196
    • Feige, U.1
  • 81
    • 0038285474 scopus 로고    scopus 로고
    • The probable value of the Lovász-Schrijver relaxations for maximum independent set
    • Feige U., and Krauthgamer R. The probable value of the Lovász-Schrijver relaxations for maximum independent set. SIAM Journal on Computing 32 (2003) 345-370
    • (2003) SIAM Journal on Computing , vol.32 , pp. 345-370
    • Feige, U.1    Krauthgamer, R.2
  • 84
    • 0036099092 scopus 로고    scopus 로고
    • On the optimality of the random hyperplane rounding technique for MAX CUT
    • Feige U., and Schechtman G. On the optimality of the random hyperplane rounding technique for MAX CUT. Random Structures and Algorithms 20 (2002) 403-440
    • (2002) Random Structures and Algorithms , vol.20 , pp. 403-440
    • Feige, U.1    Schechtman, G.2
  • 85
    • 0042158972 scopus 로고
    • Bounds for eigenvalues of doubly stochastic matrices
    • Fiedler M. Bounds for eigenvalues of doubly stochastic matrices. Linear Algebra and its Applications 5 (1972) 299-310
    • (1972) Linear Algebra and its Applications , vol.5 , pp. 299-310
    • Fiedler, M.1
  • 88
    • 0346613559 scopus 로고    scopus 로고
    • Improved approximation algorithms for MAX k-CUT and MAX BISECTION
    • [Preliminary version in Proceedings of the 4th International IPCO Conference, Copenhagen, Lecture Notes in Computer Science, 920, 1-13, 1995.]
    • Frieze A., and Jerrum M. Improved approximation algorithms for MAX k-CUT and MAX BISECTION. Algorithmica 18 (1997) 67-81 [Preliminary version in Proceedings of the 4th International IPCO Conference, Copenhagen, Lecture Notes in Computer Science, 920, 1-13, 1995.]
    • (1997) Algorithmica , vol.18 , pp. 67-81
    • Frieze, A.1    Jerrum, M.2
  • 89
    • 0000201892 scopus 로고    scopus 로고
    • Semidefinite programming relaxation for nonconvex quadratic programs
    • Fujie T., and Kojima M. Semidefinite programming relaxation for nonconvex quadratic programs. Journal of Global Optimization 10 (1997) 367-380
    • (1997) Journal of Global Optimization , vol.10 , pp. 367-380
    • Fujie, T.1    Kojima, M.2
  • 92
    • 0000457427 scopus 로고    scopus 로고
    • Semidefinite programming in combinatorial optimization
    • Goemans M.X. Semidefinite programming in combinatorial optimization. Mathematical Programming (1997) 143-161
    • (1997) Mathematical Programming , pp. 143-161
    • Goemans, M.X.1
  • 93
    • 0347504564 scopus 로고    scopus 로고
    • Semidefinite programs and association schemes
    • Goemans M., and Rendl F. Semidefinite programs and association schemes. Computing 63 (1999) 331-340
    • (1999) Computing , vol.63 , pp. 331-340
    • Goemans, M.1    Rendl, F.2
  • 94
    • 0035518191 scopus 로고    scopus 로고
    • When does the positive semidefiniteness constraint help in lifting procedures?
    • Goemans M.X., and Tunçel L. When does the positive semidefiniteness constraint help in lifting procedures?. Mathematics of Operations Research 26 (2001) 796-815
    • (2001) Mathematics of Operations Research , vol.26 , pp. 796-815
    • Goemans, M.X.1    Tunçel, L.2
  • 95
    • 0000175256 scopus 로고
    • New 3/4-approximation algorithms for the maximum satisfiability problem
    • Goemans M.X., and Williamson D.P. New 3/4-approximation algorithms for the maximum satisfiability problem. SIAM Journal on Discrete Mathematics 7 (1994) 656-666
    • (1994) SIAM Journal on Discrete Mathematics , vol.7 , pp. 656-666
    • Goemans, M.X.1    Williamson, D.P.2
  • 96
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cuts and satisfiability problems using semidefinite programming
    • [Preliminary version in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, ACM, New York, pp. 422-431, 1994.]
    • Goemans M.X., and Williamson D.P. Improved approximation algorithms for maximum cuts and satisfiability problems using semidefinite programming. Journal of the Association for Computing Machinery 42 (1995) 1115-1145 [Preliminary version in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, ACM, New York, pp. 422-431, 1994.]
    • (1995) Journal of the Association for Computing Machinery , vol.42 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 103
    • 0242511176 scopus 로고    scopus 로고
    • Computational experience with stable set relaxations
    • Gruber G., and Rendl F. Computational experience with stable set relaxations. SIAM Journal on Optimization 13 (2003) 1014-1028
    • (2003) SIAM Journal on Optimization , vol.13 , pp. 1014-1028
    • Gruber, G.1    Rendl, F.2
  • 104
    • 0035185680 scopus 로고    scopus 로고
    • A characterization of weakly bipartite graphs
    • Guenin B. A characterization of weakly bipartite graphs. Journal of Combinatorial Theory B 81 (2001) 112-168
    • (2001) Journal of Combinatorial Theory B , vol.81 , pp. 112-168
    • Guenin, B.1
  • 105
    • 0000290202 scopus 로고
    • A new lower bound via projection for the quadratic assignment problem
    • Hadley S.W., Rendl F., and Wolkowicz H. A new lower bound via projection for the quadratic assignment problem. Mathematics of Operations Research 17 (1992) 727-739
    • (1992) Mathematics of Operations Research , vol.17 , pp. 727-739
    • Hadley, S.W.1    Rendl, F.2    Wolkowicz, H.3
  • 106
    • 0027201216 scopus 로고
    • A still better performance guarantee for approximate graph coloring
    • Halldórsson M.M. A still better performance guarantee for approximate graph coloring. Information Processing Letters 45 (1993) 19-23
    • (1993) Information Processing Letters , vol.45 , pp. 19-23
    • Halldórsson, M.M.1
  • 107
    • 84958967409 scopus 로고    scopus 로고
    • Approximations of independent sets in graphs
    • Jansen K., and Rolim J. (Eds)
    • Halldórsson M.M. Approximations of independent sets in graphs. In: Jansen K., and Rolim J. (Eds). APPROX '98, Lecture Notes in Computer Science 1444 (1998) 1-14
    • (1998) APPROX '98, Lecture Notes in Computer Science , vol.1444 , pp. 1-14
    • Halldórsson, M.M.1
  • 108
    • 70350641953 scopus 로고    scopus 로고
    • Approximations of weighted independent sets and hereditary subset problems
    • Asano T., et al. (Ed)
    • Halldórsson M.M. Approximations of weighted independent sets and hereditary subset problems. In: Asano T., et al. (Ed). COCOON '99, Lecture Notes in Computer Science 1627 (1999) 261-270
    • (1999) COCOON '99, Lecture Notes in Computer Science , vol.1627 , pp. 261-270
    • Halldórsson, M.M.1
  • 109
    • 0036588838 scopus 로고    scopus 로고
    • Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
    • [Preliminary version in Proceedings of 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 329-337, 2000.]
    • Halperin E. Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs. SIAM Journal on Computing 31 (2002) 1608-1623 [Preliminary version in Proceedings of 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 329-337, 2000.]
    • (2002) SIAM Journal on Computing , vol.31 , pp. 1608-1623
    • Halperin, E.1
  • 112
    • 84947262091 scopus 로고    scopus 로고
    • A unified framework for obtaining improved approximations algorithms for maximum graph bisection problems
    • Aardal K., and Gerards A.M.H. (Eds)
    • Halperin E., and Zwick U. A unified framework for obtaining improved approximations algorithms for maximum graph bisection problems. In: Aardal K., and Gerards A.M.H. (Eds). IPCO 2001, Lecture Notes in Computer Science 2081 (2001) 210-225
    • (2001) IPCO 2001, Lecture Notes in Computer Science , vol.2081 , pp. 210-225
    • Halperin, E.1    Zwick, U.2
  • 113
    • 0013189831 scopus 로고    scopus 로고
    • Approximation algorithms for MAX 4-SAT and rounding procedures for semidefinite programs
    • [Preliminary version in Proceedings of the 7th conference on Integer Programming and Combinatorial Optimization, Graz, Austria, pp. 202-217, 1999.]
    • Halperin E., and Zwick U. Approximation algorithms for MAX 4-SAT and rounding procedures for semidefinite programs. Journal of Algorithms 40 (2001) 184-211 [Preliminary version in Proceedings of the 7th conference on Integer Programming and Combinatorial Optimization, Graz, Austria, pp. 202-217, 1999.]
    • (2001) Journal of Algorithms , vol.40 , pp. 184-211
    • Halperin, E.1    Zwick, U.2
  • 115
    • 0030671781 scopus 로고    scopus 로고
    • Håstad, J. (1997). Some optimal inapproximability results. In Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, ACM, New York, pp. 1-10. [Full version in Electronic Colloquium on Computational Complexity, Report TR97-037.]
    • Håstad, J. (1997). Some optimal inapproximability results. In Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, ACM, New York, pp. 1-10. [Full version in Electronic Colloquium on Computational Complexity, Report TR97-037.]
  • 119
    • 84972526350 scopus 로고
    • The variation of the spectrum of a normal matrix
    • Hoffman A.J., and Wielandt H.W. The variation of the spectrum of a normal matrix. Duke Mathematical Journal 20 (1953) 37-39
    • (1953) Duke Mathematical Journal , vol.20 , pp. 37-39
    • Hoffman, A.J.1    Wielandt, H.W.2
  • 123
    • 0016349356 scopus 로고
    • Approximation algorithms for combinatorial problems
    • Johnson D. Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9 (1974) 256-278
    • (1974) Journal of Computer and System Sciences , vol.9 , pp. 256-278
    • Johnson, D.1
  • 126
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph colouring by semidefinite programming
    • [Preliminary version in Proceedings of 35th IEEE Symposium on Foundations of Computer Science, IEEE Computer Science Press, Los Alamitos, CA, pages 2-13, 1994.]
    • Karger D., Motwani R., and Sudan M. Approximate graph colouring by semidefinite programming. Journal of the Association for Computing Machinery 45 (1998) 246-265 [Preliminary version in Proceedings of 35th IEEE Symposium on Foundations of Computer Science, IEEE Computer Science Press, Los Alamitos, CA, pages 2-13, 1994.]
    • (1998) Journal of the Association for Computing Machinery , vol.45 , pp. 246-265
    • Karger, D.1    Motwani, R.2    Sudan, M.3
  • 127
    • 0343168152 scopus 로고    scopus 로고
    • How good is the Goemans-Williamson max-cut algorithm?
    • Karloff H. How good is the Goemans-Williamson max-cut algorithm?. SIAM Journal on Computing 29 (1999) 336-350
    • (1999) SIAM Journal on Computing , vol.29 , pp. 336-350
    • Karloff, H.1
  • 129
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • Plenum Press, New York
    • Karp R.M. Reducibility among combinatorial problems. Complexity of Computer Computations (1972), Plenum Press, New York 85-103
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 130
    • 0031351353 scopus 로고    scopus 로고
    • Computing integral points in convex semi-algebraic sets
    • IEEE Computer Science Press, Los Alamitos, CA
    • Khachiyan L., and Porkolab L. Computing integral points in convex semi-algebraic sets. 38th Annual Symposium on Foundations of Computer Science (1997), IEEE Computer Science Press, Los Alamitos, CA 162-171
    • (1997) 38th Annual Symposium on Foundations of Computer Science , pp. 162-171
    • Khachiyan, L.1    Porkolab, L.2
  • 132
    • 0039550370 scopus 로고    scopus 로고
    • On the hardness of approximating the chromatic number
    • [Preliminary version in Proceedings of the 2nd Israel Symposium on Theory and Computing Systems, IEEE Computer Society Press, Los Alamos, CA, pp. 250-260, 1993.]
    • Khanna S., Linial N., and Safra S. On the hardness of approximating the chromatic number. Combinatorica 20 (2000) 393-415 [Preliminary version in Proceedings of the 2nd Israel Symposium on Theory and Computing Systems, IEEE Computer Society Press, Los Alamos, CA, pp. 250-260, 1993.]
    • (2000) Combinatorica , vol.20 , pp. 393-415
    • Khanna, S.1    Linial, N.2    Safra, S.3
  • 133
    • 0011190325 scopus 로고    scopus 로고
    • The Lovász theta function and a semidefinite programming relaxation of vertex cover
    • Kleinberg J., and Goemans M.X. The Lovász theta function and a semidefinite programming relaxation of vertex cover. SIAM Journal on Discrete Mathematics 11 (1998) 196-204
    • (1998) SIAM Journal on Discrete Mathematics , vol.11 , pp. 196-204
    • Kleinberg, J.1    Goemans, M.X.2
  • 135
    • 33947499212 scopus 로고    scopus 로고
    • A PTAS for the minimization of polynomials of fixed degree over the simplex
    • Preprint
    • de Klerk, E., M. Laurent, P. Parrilo (2004). A PTAS for the minimization of polynomials of fixed degree over the simplex. Preprint
    • (2004)
    • de Klerk, E.1    Laurent, M.2    Parrilo, P.3
  • 136
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • de Klerk E., and Pasechnik D.V. Approximation of the stability number of a graph via copositive programming. SIAM Journal on Optimization 12 (2002) 875-892
    • (2002) SIAM Journal on Optimization , vol.12 , pp. 875-892
    • de Klerk, E.1    Pasechnik, D.V.2
  • 138
    • 0344794583 scopus 로고    scopus 로고
    • Relaxations of the satisfiability problem using semidefinite programming
    • de Klerk E., Warners J.P., and van Maaren H. Relaxations of the satisfiability problem using semidefinite programming. Journal of Automated Reasoning 24 (2000) 37-65
    • (2000) Journal of Automated Reasoning , vol.24 , pp. 37-65
    • de Klerk, E.1    Warners, J.P.2    van Maaren, H.3
  • 140
    • 0031542833 scopus 로고    scopus 로고
    • Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices
    • Kojima M., Shindoh S., and Hara S. Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM Journal on Optimization 7 (1997) 86-125
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 86-125
    • Kojima, M.1    Shindoh, S.2    Hara, S.3
  • 141
    • 0040214558 scopus 로고    scopus 로고
    • Cones of matrices and successive convex relaxations of nonconvex sets
    • Kojima M., and Tunçel L. Cones of matrices and successive convex relaxations of nonconvex sets. SIAM Journal on Optimization 10 (2000) 750-778
    • (2000) SIAM Journal on Optimization , vol.10 , pp. 750-778
    • Kojima, M.1    Tunçel, L.2
  • 143
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre J.B. Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization 11 (2001) 796-817
    • (2001) SIAM Journal on Optimization , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 144
    • 39649093787 scopus 로고    scopus 로고
    • An explicit exact SDP relaxation for nonlinear 0 - 1 programs
    • Aardal K., and Gerards A.M.H. (Eds) [See also: An explicit equivalent positive semidefinite program for nonlinear 0-1 programs. SIAM Journal on Optimization 12, 756-769, 2002.]
    • Lasserre J.B. An explicit exact SDP relaxation for nonlinear 0 - 1 programs. In: Aardal K., and Gerards A.M.H. (Eds). IPCO 2001, Lecture Notes in Computer Science 2081 (2001) 293-303 [See also: An explicit equivalent positive semidefinite program for nonlinear 0-1 programs. SIAM Journal on Optimization 12, 756-769, 2002.]
    • (2001) IPCO 2001, Lecture Notes in Computer Science , vol.2081 , pp. 293-303
    • Lasserre, J.B.1
  • 145
    • 0036577765 scopus 로고    scopus 로고
    • Semidefinite programming vs. LP relaxations for polynomial programming
    • Lasserre J.B. Semidefinite programming vs. LP relaxations for polynomial programming. Mathematics of Operations Research 27 (2002) 347-360
    • (2002) Mathematics of Operations Research , vol.27 , pp. 347-360
    • Lasserre, J.B.1
  • 146
    • 0039506352 scopus 로고    scopus 로고
    • The real positive semidefinite completion problem for series-parallel graphs
    • Laurent M. The real positive semidefinite completion problem for series-parallel graphs. Linear Algebra and its Applications 252 (1997) 347-366
    • (1997) Linear Algebra and its Applications , vol.252 , pp. 347-366
    • Laurent, M.1
  • 147
    • 0042859913 scopus 로고    scopus 로고
    • A connection between positive semidefinite and Euclidean distance matrix completion problems
    • Laurent M. A connection between positive semidefinite and Euclidean distance matrix completion problems. Linear Algebra and its Applications 273 (1998) 9-22
    • (1998) Linear Algebra and its Applications , vol.273 , pp. 9-22
    • Laurent, M.1
  • 148
    • 77950469772 scopus 로고    scopus 로고
    • Laurent, M. (1998b). A tour d'horizon on positive semidefinite and Euclidean distance matrix completion problems, in: P. Pardalos, H. Wolkowicz (eds.), Topics in Semidefinite and Interior-Point Methods, 18 of the Fields Institute for Research in Mathematical Science, Communication Series, Providence, Rhode Island, pp. 51-76
    • Laurent, M. (1998b). A tour d'horizon on positive semidefinite and Euclidean distance matrix completion problems, in: P. Pardalos, H. Wolkowicz (eds.), Topics in Semidefinite and Interior-Point Methods, Vol. 18 of the Fields Institute for Research in Mathematical Science, Communication Series, Providence, Rhode Island, pp. 51-76
  • 149
    • 0035219189 scopus 로고    scopus 로고
    • Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems
    • Laurent M. Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems. SIAM Journal on Matrix Analysis and its Applications 22 (2000) 874-894
    • (2000) SIAM Journal on Matrix Analysis and its Applications , vol.22 , pp. 874-894
    • Laurent, M.1
  • 150
    • 0040489291 scopus 로고    scopus 로고
    • On the sparsity order of a graph and its deficiency in chordality
    • Laurent M. On the sparsity order of a graph and its deficiency in chordality. Combinatorica 21 (2001) 543-570
    • (2001) Combinatorica , vol.21 , pp. 543-570
    • Laurent, M.1
  • 151
    • 0036013026 scopus 로고    scopus 로고
    • Tighter linear and semidefinite relaxations for max-cut based on the Lovász-Schrijver lift-and-project procedure
    • Laurent M. Tighter linear and semidefinite relaxations for max-cut based on the Lovász-Schrijver lift-and-project procedure. SIAM Journal on Optimization 12 (2001) 345-375
    • (2001) SIAM Journal on Optimization , vol.12 , pp. 345-375
    • Laurent, M.1
  • 152
    • 0141517272 scopus 로고    scopus 로고
    • A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0, 1-programming
    • Laurent M. A comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0, 1-programming. Mathematics of Operations Research 28 3 (2003) 470-496
    • (2003) Mathematics of Operations Research , vol.28 , Issue.3 , pp. 470-496
    • Laurent, M.1
  • 153
    • 3142703556 scopus 로고    scopus 로고
    • Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope
    • Laurent M. Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope. Mathematical of Operations Reaserch 28 4 (2003) 871-883
    • (2003) Mathematical of Operations Reaserch , vol.28 , Issue.4 , pp. 871-883
    • Laurent, M.1
  • 155
    • 4243480492 scopus 로고
    • On a positive semidefinite relaxation of the cut polytope
    • Laurent M., and Poljak S. On a positive semidefinite relaxation of the cut polytope. Linear Algebra and its Applications 223/224 (1995) 439-461
    • (1995) Linear Algebra and its Applications , vol.223-224 , pp. 439-461
    • Laurent, M.1    Poljak, S.2
  • 157
    • 0031144411 scopus 로고    scopus 로고
    • Connections between semidefinite relaxations of the max-cut and stable set problems
    • Laurent M., Poljak S., and Rendl F. Connections between semidefinite relaxations of the max-cut and stable set problems. Mathematical Programming 77 (1997) 225-246
    • (1997) Mathematical Programming , vol.77 , pp. 225-246
    • Laurent, M.1    Poljak, S.2    Rendl, F.3
  • 158
    • 0020845921 scopus 로고
    • Integer programming with a fixed number of variables
    • Lenstra Jr. H.W. Integer programming with a fixed number of variables. Mathematics of Operations Research 8 (1983) 538-548
    • (1983) Mathematics of Operations Research , vol.8 , pp. 538-548
    • Lenstra Jr., H.W.1
  • 159
    • 84868631424 scopus 로고    scopus 로고
    • Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems
    • Cook W.J., and Schulz A.S. (Eds)
    • Lewin M., Livnat D., and Zwick U. Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems. In: Cook W.J., and Schulz A.S. (Eds). IPCO 2002, Lecture Notes in Computer Science 2337 (2002) 67-82
    • (2002) IPCO 2002, Lecture Notes in Computer Science , vol.2337 , pp. 67-82
    • Lewin, M.1    Livnat, D.2    Zwick, U.3
  • 160
    • 0000652415 scopus 로고
    • The geometry of graphs and some of its algorithmic consequences
    • Linial N., London E., and Rabinovich Yu. The geometry of graphs and some of its algorithmic consequences. Combinatorica 15 (1995) 215-245
    • (1995) Combinatorica , vol.15 , pp. 215-245
    • Linial, N.1    London, E.2    Rabinovich, Yu.3
  • 162
  • 163
    • 79959971337 scopus 로고    scopus 로고
    • Stable set problem and the lift-and-project ranks of graphs
    • Lipták L., and Tunçel L. Stable set problem and the lift-and-project ranks of graphs. Mathematical Programming Ser. B 98 (2003) 319-353
    • (2003) Mathematical Programming Ser. B , vol.98 , pp. 319-353
    • Lipták, L.1    Tunçel, L.2
  • 165
    • 49649140846 scopus 로고
    • Normal hypergraphs and the perfect graph conjecture
    • Lovász L. Normal hypergraphs and the perfect graph conjecture. Discrete Mathematics 2 (1972) 253-267
    • (1972) Discrete Mathematics , vol.2 , pp. 253-267
    • Lovász, L.1
  • 167
    • 38149146720 scopus 로고
    • Stable sets and polynomials
    • Lovász L. Stable sets and polynomials. Discrete Mathematics 124 (1994) 137-153
    • (1994) Discrete Mathematics , vol.124 , pp. 137-153
    • Lovász, L.1
  • 168
    • 30744463727 scopus 로고    scopus 로고
    • Semidefinite programs and combinatorial optimization
    • Reed B.A., and Sales C.L. (Eds), CMS Books in Mathematics, Springer
    • Lovász L. Semidefinite programs and combinatorial optimization. In: Reed B.A., and Sales C.L. (Eds). Recent Advances in Algorithms and Combinatorics (2003), CMS Books in Mathematics, Springer 137-194
    • (2003) Recent Advances in Algorithms and Combinatorics , pp. 137-194
    • Lovász, L.1
  • 169
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • Lovász L., and Schrijver A. Cones of matrices and set-functions and 0-1 optimization. SIAM Journal on Optimization 1 (1991) 166-190
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 172
    • 0029493083 scopus 로고
    • Derandomizing semidefinite programming based approximation algorithms
    • IEEE Computer Science Press, Los Alamitos, CA
    • Mahajan S., and Ramesh H. Derandomizing semidefinite programming based approximation algorithms. Proceedings of the 36th Symposium on Foundations of Computer Science (1995), IEEE Computer Science Press, Los Alamitos, CA 162-169
    • (1995) Proceedings of the 36th Symposium on Foundations of Computer Science , pp. 162-169
    • Mahajan, S.1    Ramesh, H.2
  • 176
    • 77950468768 scopus 로고    scopus 로고
    • Strenghtening the Lovász θ{symbol}({A figure is presented}) bound for graph colouring. Preprint
    • to appear
    • Meurdesoif, P. (2000). Strenghtening the Lovász θ{symbol}({A figure is presented}) bound for graph colouring. Preprint, [Mathematical Programming, to appear]
    • (2000) Mathematical Programming
    • Meurdesoif, P.1
  • 178
    • 0031285899 scopus 로고    scopus 로고
    • Primal-dual path-following algorithms for semidefinite programming
    • Monteiro R.D.C. Primal-dual path-following algorithms for semidefinite programming. SIAM Journal on Optimization 7 (1997) 663-678
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 663-678
    • Monteiro, R.D.C.1
  • 179
    • 0000230999 scopus 로고
    • Maxima for graphs and a new proof of a theorem of Túran
    • Motzkin T.S., and Straus E.G. Maxima for graphs and a new proof of a theorem of Túran. Canadian Journal of Mathematics 17 (1965) 533-540
    • (1965) Canadian Journal of Mathematics , vol.17 , pp. 533-540
    • Motzkin, T.S.1    Straus, E.G.2
  • 180
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and linear programming
    • Murty K.G., and Kabadi S.N. Some NP-complete problems in quadratic and linear programming. Mathematical Programming 39 (1987) 117-129
    • (1987) Mathematical Programming , vol.39 , pp. 117-129
    • Murty, K.G.1    Kabadi, S.N.2
  • 183
    • 0031681870 scopus 로고    scopus 로고
    • Semidefinite relaxation and nonconvex quadratic optimization
    • Nesterov Y. Semidefinite relaxation and nonconvex quadratic optimization. Optimization Methods and Software 9 (1998) 141-160
    • (1998) Optimization Methods and Software , vol.9 , pp. 141-160
    • Nesterov, Y.1
  • 184
    • 0001776805 scopus 로고    scopus 로고
    • Squared functional systems and optimization problems
    • Frenk J.B.G., Roos C., Terlaky T., and Zhang S. (Eds), Kluwer Academic Publishers
    • Nesterov Y. Squared functional systems and optimization problems. In: Frenk J.B.G., Roos C., Terlaky T., and Zhang S. (Eds). High Performance Optimization (2000), Kluwer Academic Publishers 405-440
    • (2000) High Performance Optimization , pp. 405-440
    • Nesterov, Y.1
  • 185
    • 0000011340 scopus 로고
    • Some matrix inequalities and metrization of matrix space
    • (reprinted in: John von Neumann: Collected works, Vol. 4, A. H. Taub ed., MacMillan, 205-219, 1962.)
    • von Neumann J. Some matrix inequalities and metrization of matrix space. Tomsk Univ. Rev. 1 (1937) 286-300, (reprinted in: John von Neumann: Collected works, Vol. 4, A. H. Taub ed., MacMillan, 205-219, 1962.)
    • (1937) Tomsk Univ. Rev. , vol.1 , pp. 286-300
    • von Neumann, J.1
  • 186
    • 0000965291 scopus 로고
    • An experimental comparison of techniques for the assignment of facilities to locations
    • Nugent C.E., Vollman T.E., and Ruml J. An experimental comparison of techniques for the assignment of facilities to locations. Operations Research 16 (1968) 150-173
    • (1968) Operations Research , vol.16 , pp. 150-173
    • Nugent, C.E.1    Vollman, T.E.2    Ruml, J.3
  • 188
    • 77950504463 scopus 로고    scopus 로고
    • Topics in semidefinite programming and interior point methods
    • Pardalos P.M., and Wolkowicz H. (Eds), American Mathematical Society
    • Topics in semidefinite programming and interior point methods. In: Pardalos P.M., and Wolkowicz H. (Eds). Fields Institute Communications 18 (1998), American Mathematical Society
    • (1998) Fields Institute Communications 18
  • 190
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Parrilo P.A. Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming Ser. B 96 (2003) 293-320
    • (2003) Mathematical Programming Ser. B , vol.96 , pp. 293-320
    • Parrilo, P.A.1
  • 192
    • 21344441658 scopus 로고    scopus 로고
    • Cone-LP's and semidefinite programs: geometry and a simplex-type methods
    • Cunningham W.H., MacCormick S.T., and Queyranne M. (Eds)
    • Pataki G. Cone-LP's and semidefinite programs: geometry and a simplex-type methods. In: Cunningham W.H., MacCormick S.T., and Queyranne M. (Eds). IPCO 1996, Lecture Notes in Computer Science 1084 (1996) 162-174
    • (1996) IPCO 1996, Lecture Notes in Computer Science , vol.1084 , pp. 162-174
    • Pataki, G.1
  • 193
    • 0032070507 scopus 로고    scopus 로고
    • On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues
    • Pataki G. On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues. Mathematics of Operations Research 23 (1998) 339-358
    • (1998) Mathematics of Operations Research , vol.23 , pp. 339-358
    • Pataki, G.1
  • 194
    • 77950490273 scopus 로고    scopus 로고
    • Poljak, S. (1991). Polyhedral and eigenvalue approximations of the max-cut problem, in: Sets, Graphs, and Numbers, 60 of Colloquia Mathematica Societatis János Bolyai, Budapest, Hungary, pp. 569-581
    • Poljak, S. (1991). Polyhedral and eigenvalue approximations of the max-cut problem, in: Sets, Graphs, and Numbers, Vol. 60 of Colloquia Mathematica Societatis János Bolyai, Budapest, Hungary, pp. 569-581
  • 195
    • 0001469422 scopus 로고
    • Nonpolyhedral relaxations of graph-bisection problems
    • Poljak S., and Rendl F. Nonpolyhedral relaxations of graph-bisection problems. SIAM Journal on Optimization 5 (1995) 467-487
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 467-487
    • Poljak, S.1    Rendl, F.2
  • 196
    • 0041837225 scopus 로고
    • The expected relative error of the polyhedral approximation of the max-cut problem
    • Poljak S., and Tuza Z. The expected relative error of the polyhedral approximation of the max-cut problem. Operations Research Letters 16 (1994) 191-198
    • (1994) Operations Research Letters , vol.16 , pp. 191-198
    • Poljak, S.1    Tuza, Z.2
  • 199
    • 0001276275 scopus 로고    scopus 로고
    • A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra
    • Powers V., and Reznick B. A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra. Journal of Pure and Applied Algebra 164 (2001) 221-229
    • (2001) Journal of Pure and Applied Algebra , vol.164 , pp. 221-229
    • Powers, V.1    Reznick, B.2
  • 200
  • 201
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • Putinar M. Positive polynomials on compact semi-algebraic sets. Indiana University Mathematics Journal 42 (1993) 969-984
    • (1993) Indiana University Mathematics Journal , vol.42 , pp. 969-984
    • Putinar, M.1
  • 203
    • 0031146175 scopus 로고    scopus 로고
    • An exact duality theory for semidefinite programming and its complexity implications
    • Ramana M.V. An exact duality theory for semidefinite programming and its complexity implications. Mathematical Programming 77 (1997) 129-162
    • (1997) Mathematical Programming , vol.77 , pp. 129-162
    • Ramana, M.V.1
  • 204
  • 207
    • 0000334878 scopus 로고    scopus 로고
    • Semidefinite programming and combinatorial optimization
    • Rendl F. Semidefinite programming and combinatorial optimization. Applied Numerical Mathematics 29 (1999) 255-281
    • (1999) Applied Numerical Mathematics , vol.29 , pp. 255-281
    • Rendl, F.1
  • 208
    • 85025505234 scopus 로고
    • On the computational complexity and geometry of the first order theory of the reals
    • Renegar J. On the computational complexity and geometry of the first order theory of the reals. Journal of Symbolic Computation 13 3 (1992) 255-352
    • (1992) Journal of Symbolic Computation , vol.13 , Issue.3 , pp. 255-352
    • Renegar, J.1
  • 209
    • 0018492534 scopus 로고
    • A comparison of the Delsarte and Lovász bounds
    • Schrijver A. A comparison of the Delsarte and Lovász bounds. IEEE Transactions on Information Theory IT-25 (1979) 425-429
    • (1979) IEEE Transactions on Information Theory , vol.IT-25 , pp. 425-429
    • Schrijver, A.1
  • 211
    • 0036311368 scopus 로고    scopus 로고
    • A short proof of Guenin's characterization of weakly bipartite graphs
    • Schrijver A. A short proof of Guenin's characterization of weakly bipartite graphs. Journal of Combinatorial Theory B 85 (2002) 255-260
    • (2002) Journal of Combinatorial Theory B , vol.85 , pp. 255-260
    • Schrijver, A.1
  • 213
    • 0000327178 scopus 로고
    • The matroids with the max-flow min-cut property
    • Seymour P.D. The matroids with the max-flow min-cut property. Journal of Combinatorial Theory B 23 (1977) 189-222
    • (1977) Journal of Combinatorial Theory B , vol.23 , pp. 189-222
    • Seymour, P.D.1
  • 214
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • Sherali H., and Adams W. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM Journal on Discrete Mathematics 3 (1990) 411-430
    • (1990) SIAM Journal on Discrete Mathematics , vol.3 , pp. 411-430
    • Sherali, H.1    Adams, W.2
  • 215
    • 0002500749 scopus 로고
    • A hierarchy of relaxations and convex hull representations for mixed-integer zero-one programming problems
    • Sherali H., and Adams W. A hierarchy of relaxations and convex hull representations for mixed-integer zero-one programming problems. Discrete Applied Mathematics 52 (1994) 83-106
    • (1994) Discrete Applied Mathematics , vol.52 , pp. 83-106
    • Sherali, H.1    Adams, W.2
  • 217
    • 0001642333 scopus 로고
    • A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique
    • Sherali H., and Tuncbilek C.H. A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. Journal of Global Optimization 2 (1992) 101-112
    • (1992) Journal of Global Optimization , vol.2 , pp. 101-112
    • Sherali, H.1    Tuncbilek, C.H.2
  • 218
    • 0009656296 scopus 로고    scopus 로고
    • Reformulation-linearization/convexification relaxations for univariate and multivariate polynomial programming problems
    • Sherali H.D., and Tuncbilek C.H. Reformulation-linearization/convexification relaxations for univariate and multivariate polynomial programming problems. Operations Research Letters 21 (1997) 1-10
    • (1997) Operations Research Letters , vol.21 , pp. 1-10
    • Sherali, H.D.1    Tuncbilek, C.H.2
  • 219
    • 0041139522 scopus 로고
    • An approach to obtaining global extremums in polynomial mathematical programming problems
    • Shor N.Z. An approach to obtaining global extremums in polynomial mathematical programming problems. Kibernetika 5 (1987) 102-106
    • (1987) Kibernetika , vol.5 , pp. 102-106
    • Shor, N.Z.1
  • 220
    • 0000604097 scopus 로고
    • Class of global minimum bounds of polynomial functions
    • [Translated from Kibernetika, 6, 9-11, 1987.]
    • Shor N.Z. Class of global minimum bounds of polynomial functions. Cybernetics 6 (1987) 731-734 [Translated from Kibernetika, 6, 9-11, 1987.]
    • (1987) Cybernetics , vol.6 , pp. 731-734
    • Shor, N.Z.1
  • 222
    • 0000093702 scopus 로고    scopus 로고
    • Convex quadratic and semidefinite programming relaxations in scheduling
    • Skutella M. Convex quadratic and semidefinite programming relaxations in scheduling. Journal of the Association for Computing Machinery 48 (2001) 206-242
    • (2001) Journal of the Association for Computing Machinery , vol.48 , pp. 206-242
    • Skutella, M.1
  • 224
    • 34250416099 scopus 로고
    • A Nullstellensatz and a Positivstellensatz in semialgebraic geometry
    • Stengle G. A Nullstellensatz and a Positivstellensatz in semialgebraic geometry. Mathematische Annalen 207 (1974) 87-97
    • (1974) Mathematische Annalen , vol.207 , pp. 87-97
    • Stengle, G.1
  • 225
    • 0344642581 scopus 로고    scopus 로고
    • On a representation of the matching polytope via semidefinite liftings
    • Stephen T., and Tunçel L. On a representation of the matching polytope via semidefinite liftings. Mathematics of Operations Research 24 (1999) 1-7
    • (1999) Mathematics of Operations Research , vol.24 , pp. 1-7
    • Stephen, T.1    Tunçel, L.2
  • 226
    • 0003117049 scopus 로고
    • A note on the θ{symbol} number of Lovász and the generalized Delsarte bound
    • IEEE Computer Science Press, Los Alamitos, CA
    • Szegedy M. A note on the θ{symbol} number of Lovász and the generalized Delsarte bound. Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science (1994), IEEE Computer Science Press, Los Alamitos, CA 36-39
    • (1994) Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science , pp. 36-39
    • Szegedy, M.1
  • 227
    • 0033296734 scopus 로고    scopus 로고
    • A study of search directions directions in primal-dual interior-point methods for semidefinite programming
    • Todd M.J. A study of search directions directions in primal-dual interior-point methods for semidefinite programming. Optimization Methods and Software 11 (1999) 1-46
    • (1999) Optimization Methods and Software , vol.11 , pp. 1-46
    • Todd, M.J.1
  • 228
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite programming
    • Todd M.J. Semidefinite programming. Acta Numerica 10 (2001) 515-560
    • (2001) Acta Numerica , vol.10 , pp. 515-560
    • Todd, M.J.1
  • 230
    • 1542351108 scopus 로고    scopus 로고
    • Further results on approximating nonconvex quadratic optimization by semidefinite programming relaxation
    • Tseng P. Further results on approximating nonconvex quadratic optimization by semidefinite programming relaxation. SIAM Journal on Optimization 14 (2003) 268-283
    • (2003) SIAM Journal on Optimization , vol.14 , pp. 268-283
    • Tseng, P.1
  • 231
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • Vandenberghe L., and Boyd S. Semidefinite programming. SIAM Review 38 (1996) 49-95
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 232
    • 0030136319 scopus 로고    scopus 로고
    • MAX-CUT has a randomized approximation scheme in dense graphs
    • de la Vega W.F. MAX-CUT has a randomized approximation scheme in dense graphs. Random Structures and Algorithms 8 (1996) 187-198
    • (1996) Random Structures and Algorithms , vol.8 , pp. 187-198
    • de la Vega, W.F.1
  • 234
    • 0020829934 scopus 로고
    • Improving the performance guarantee for approximate graph colouring
    • Wigderson A. Improving the performance guarantee for approximate graph colouring. Journal of the Association for Computing Machinery 30 (1983) 729-735
    • (1983) Journal of the Association for Computing Machinery , vol.30 , pp. 729-735
    • Wigderson, A.1
  • 235
    • 0003395487 scopus 로고    scopus 로고
    • Wolkowicz H., Saigal R., and Vandenberghe L. (Eds), Kluwer
    • In: Wolkowicz H., Saigal R., and Vandenberghe L. (Eds). Handbook of Semidefinite Programming (2000), Kluwer
    • (2000) Handbook of Semidefinite Programming
  • 237
    • 0001843554 scopus 로고
    • On the approximation of maximum satisfiability
    • Yannakakis M. On the approximation of maximum satisfiability. Journal of Algorithms 17 (1994) 475-502
    • (1994) Journal of Algorithms , vol.17 , pp. 475-502
    • Yannakakis, M.1
  • 238
    • 0000549997 scopus 로고    scopus 로고
    • Approximating quadratic programming with bound and quadratic constraints
    • Ye Y. Approximating quadratic programming with bound and quadratic constraints. Mathematical Programming 84 (1999) 219-226
    • (1999) Mathematical Programming , vol.84 , pp. 219-226
    • Ye, Y.1
  • 239
    • 0000734821 scopus 로고    scopus 로고
    • A 0.699-approximation algorithm for Max-Bisection
    • Ye Y. A 0.699-approximation algorithm for Max-Bisection. Mathematical Programming 90 (2001) 101-111
    • (2001) Mathematical Programming , vol.90 , pp. 101-111
    • Ye, Y.1
  • 240
    • 0032081158 scopus 로고    scopus 로고
    • On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming
    • Zhang Y. On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM Journal on Optimization 8 (1998) 365-386
    • (1998) SIAM Journal on Optimization , vol.8 , pp. 365-386
    • Zhang, Y.1
  • 241
    • 0038029207 scopus 로고    scopus 로고
    • Quadratic minimization and semidefinite relaxation
    • Zhang S. Quadratic minimization and semidefinite relaxation. Mathematical Progamming 87 (2000) 453-465
    • (2000) Mathematical Progamming , vol.87 , pp. 453-465
    • Zhang, S.1
  • 243
    • 0032631766 scopus 로고    scopus 로고
    • Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems
    • ACM, New York
    • Zwick U. Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems. Proceedings of the 31st Annual ACM Symposium on Theory of Computing (1999), ACM, New York 679-687
    • (1999) Proceedings of the 31st Annual ACM Symposium on Theory of Computing , pp. 679-687
    • Zwick, U.1


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