메뉴 건너뛰기




Volumn 10, Issue 3, 2000, Pages 750-778

Cones of matrices and successive convex relaxations of nonconvex sets

Author keywords

Bilinear matrix inequality; Global optimization; Linear matrix inequality; Nonconvex quadratic optimization problem; Semi infinite programming; Semidefinite programming

Indexed keywords


EID: 0040214558     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623498336450     Document Type: Article
Times cited : (58)

References (29)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization
    • F. ALIZADEH, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim., 5 (1995), pp. 13-51.
    • (1995) SIAM J. Optim. , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 2
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • E. BALAS, S. CERIA, AND G. CORNUÉJOLS, A lift-and-project cutting plane algorithm for mixed 0-1 programs, Math. Programming, 58 (1993), pp. 295-323.
    • (1993) Math. Programming , vol.58 , pp. 295-323
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 3
    • 0003004622 scopus 로고
    • Linear matrix inequalities in system and control theory
    • SIAM, Philadelphia
    • S. BOYD, L. EL GHAOUI, E. FERON, AND V. BALAKRISHNAN, Linear Matrix Inequalities in System and Control Theory, Stud. Appl. Math. 15, SIAM, Philadelphia, 1994.
    • (1994) Stud. Appl. Math. , vol.15
    • Boyd, S.1    El Ghaoui, L.2    Feron, E.3    Balakrishnan, V.4
  • 5
    • 84972015971 scopus 로고
    • The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space
    • G. EWALD, D. G. LARMAN, AND C. A. ROGERS, The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space, Mathematika, 17 (1970), pp. 1-20.
    • (1970) Mathematika , vol.17 , pp. 1-20
    • Ewald, G.1    Larman, D.G.2    Rogers, C.A.3
  • 6
    • 0000201892 scopus 로고    scopus 로고
    • Semidefinite relaxation for nonconvex programs
    • T. FUJIE AND M. KOJIMA, Semidefinite relaxation for nonconvex programs, J. Global Optim., 10 (1997), pp. 367-380.
    • (1997) J. Global Optim. , vol.10 , pp. 367-380
    • Fujie, T.1    Kojima, M.2
  • 7
    • 0000457427 scopus 로고    scopus 로고
    • Semidefinite programming in combinatorial optimization
    • M. X. GOEMANS, Semidefinite programming in combinatorial optimization, Math. Programming, 79 (1997), pp. 143-161.
    • (1997) Math. Programming , vol.79 , pp. 143-161
    • Goemans, M.X.1
  • 8
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • M. X. GOEMANS AND D. P. WILLIAMSON, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J. Assoc. Comput. Mach., 42 (1995), pp. 1115-1145.
    • (1995) J. Assoc. Comput. Mach. , vol.42 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 10
    • 0039727161 scopus 로고    scopus 로고
    • Technical Report B-341, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo, Japan, Also issued as CORR 98-34, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
    • M. KOJIMA AND L. TUNÇEL, Discretization and Localization in Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems, Technical Report B-341, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo, Japan, 1998. Also issued as CORR 98-34, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
    • (1998) Discretization and Localization in Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems
    • Kojima, M.1    Tunçel, L.2
  • 12
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • L. LOVÁSZ AND A. SCHRIJVER, Cones of matrices and set-functions and 0-1 optimization, SIAM J. Optim., 1 (1991), pp. 166-190.
    • (1991) SIAM J. Optim. , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 14
    • 0031145270 scopus 로고    scopus 로고
    • A cone programming approach to the bilinear matrix inequality problem and its geometry
    • M. MESBAHI AND G. P. PAPAVASSILOPOULOS, A cone programming approach to the bilinear matrix inequality problem and its geometry, Math. Programming, 77 (1997), pp. 247-272.
    • (1997) Math. Programming , vol.77 , pp. 247-272
    • Mesbahi, M.1    Papavassilopoulos, G.P.2
  • 15
    • 0031681870 scopus 로고    scopus 로고
    • Semidefinite relaxation and nonconvex quadratic optimization
    • YU. E. NESTEROV, Semidefinite relaxation and nonconvex quadratic optimization, Optim. Methods Softw., 9 (1998), pp. 141-160.
    • (1998) Optim. Methods Softw. , vol.9 , pp. 141-160
    • Nesterov, Yu.E.1
  • 16
    • 0003254248 scopus 로고
    • Interior-point polynomial algorithms in convex programming
    • SIAM, Philadelphia
    • YU. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, Stud. Appl. Math. 13, SIAM, Philadelphia, 1994.
    • (1994) Stud. Appl. Math. , vol.13
    • Nesterov, Yu.1    Nemirovskii, A.2
  • 17
    • 0012052634 scopus 로고    scopus 로고
    • Research Report 97-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, revised
    • G. PATAKI AND L. TUNÇEL, On the Generic Properties of Convex Optimization Problems in Conic Form, Research Report 97-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 1997, revised 1999.
    • (1997) On the Generic Properties of Convex Optimization Problems in Conic Form
    • Pataki, G.1    Tunçel, L.2
  • 18
    • 0002821681 scopus 로고
    • A recipe for semidefinite relaxation for (0,1)-quadratic programming
    • S. POLJAK, F. RENDL, AND H. WOLKOWICZ, A recipe for semidefinite relaxation for (0,1)-quadratic programming, J. Global Optim., 7 (1995), pp. 51-73.
    • (1995) J. Global Optim. , vol.7 , pp. 51-73
    • Poljak, S.1    Rendl, F.2    Wolkowicz, H.3
  • 21
    • 34249831859 scopus 로고
    • A new reformulation-linearization technique for bilinear programming problems
    • H. D. SHERALI AND A. ALAMEDDINE, A new reformulation-linearization technique for bilinear programming problems, J. Global Optim., 2 (1992), pp. 379-410.
    • (1992) J. Global Optim. , vol.2 , pp. 379-410
    • Sherali, H.D.1    Alameddine, A.2
  • 22
    • 0003374522 scopus 로고
    • A reformulation-convexification approach for solving nonconvex quadratic programming problems
    • H. D. SHERALI AND C. H. TUNCBILEK, A reformulation-convexification approach for solving nonconvex quadratic programming problems, J. Global Optim., 7 (1995), pp. 1-31.
    • (1995) J. Global Optim. , vol.7 , pp. 1-31
    • Sherali, H.D.1    Tuncbilek, C.H.2
  • 23
    • 0023454146 scopus 로고
    • Quadratic optimization problems
    • N. Z. SHOR, Quadratic optimization problems, Soviet J. Comput. Systems Sci., 25 (1987), pp. 1-11.
    • (1987) Soviet J. Comput. Systems Sci. , vol.25 , pp. 1-11
    • Shor, N.Z.1
  • 24
    • 0000834224 scopus 로고
    • Dual quadratic estimates in polynomial and boolean programming
    • N. Z. SHOR, Dual quadratic estimates in polynomial and boolean programming, Ann. Oper. Res., 25 (1990), pp. 163-168.
    • (1990) Ann. Oper. Res. , vol.25 , pp. 163-168
    • Shor, N.Z.1
  • 25
    • 0344642581 scopus 로고    scopus 로고
    • On a representation of the matching polytope via semidefinite liftings
    • T. STEPHEN AND L. TUNÇEL, On a representation of the matching polytope via semidefinite liftings, Math. Oper. Res., 24 (1999), pp. 1-7.
    • (1999) Math. Oper. Res. , vol.24 , pp. 1-7
    • Stephen, T.1    Tunçel, L.2
  • 27
    • 0001412774 scopus 로고    scopus 로고
    • Towards the implementation of successive convex relaxation method for nonconvex quadratic optimization problem
    • P. M. Pardalos, ed., Kluwer Academic Press, Dordrecht, to appear
    • A. TAKEDA Y. DAI, M. FUKUDA, AND M. KOJIMA, Towards the implementation of successive convex relaxation method for nonconvex quadratic optimization problem, in Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, P. M. Pardalos, ed., Kluwer Academic Press, Dordrecht, to appear.
    • Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems
    • Takeda, A.1    Dai, Y.2    Fukuda, M.3    Kojima, M.4
  • 28
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 29
    • 0000549997 scopus 로고    scopus 로고
    • Approximating quadratic programming with bound and quadratic constraints
    • Y. YE, Approximating quadratic programming with bound and quadratic constraints, Math. Programming, 84 (1999), pp. 219-226.
    • (1999) Math. Programming , vol.84 , pp. 219-226
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.