메뉴 건너뛰기




Volumn 124, Issue 1-2, 2010, Pages 383-411

Convex relaxations of non-convex mixed integer quadratically constrained programs: Extended formulations

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL RESULTS; CONSTRAINED PROGRAMMING; CONVEX QUADRATIC CONSTRAINTS; CONVEX RELAXATION; CUTTING PLANE ALGORITHMS; DISJUNCTIVE PROGRAMMING; EIGENVALUES; EIGENVECTORS; EXTENDED FORMULATIONS; INTEGER VARIABLES; LIFT-AND-PROJECT; MATRIX; MIXED INTEGER; NON-CONVEX CONSTRAINTS; VALID INEQUALITY;

EID: 77955175439     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-010-0371-9     Document Type: Article
Times cited : (71)

References (37)
  • 2
    • 0038706615 scopus 로고    scopus 로고
    • Disjunctive programming: Properties of the convex hull of feasible points
    • 0921.90118 10.1016/S0166-218X(98)00136-X 1663099
    • E. Balas 1998 Disjunctive programming: properties of the convex hull of feasible points Discrete Appl. Math. 89 1-3 3 44 0921.90118 10.1016/S0166- 218X(98)00136-X 1663099
    • (1998) Discrete Appl. Math. , vol.89 , Issue.13 , pp. 3-44
    • Balas, E.1
  • 3
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • 10.1007/BF01581273
    • E. Balas S. Ceria G. Cornuéjols 1993 A lift-and-project cutting plane algorithm for mixed 0-1 programs Math. Program. 58 1-3 295 324 10.1007/BF01581273
    • (1993) Math. Program. , vol.58 , Issue.13 , pp. 295-324
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 5
    • 38749096673 scopus 로고    scopus 로고
    • Optimizing over the split closure
    • DOI 10.1007/s10107-006-0049-5
    • E. Balas A. Saxena 2008 Optimizing over the split closure Math. Program. 113 2 219 240 1135.90030 10.1007/s10107-006-0049-5 2375481 (Pubitemid 351177970)
    • (2008) Mathematical Programming , vol.113 , Issue.2 , pp. 219-240
    • Balas, E.1    Saxena, A.2
  • 6
    • 0040407032 scopus 로고
    • Sequential convexification in reverse convex and disjunctive programming
    • 0683.90063 10.1007/BF01587096 1028227
    • E. Balas J. Tama J. Tind 1989 Sequential convexification in reverse convex and disjunctive programming Math. Program. 44 1-3 337 350 0683.90063 10.1007/BF01587096 1028227
    • (1989) Math. Program. , vol.44 , Issue.13 , pp. 337-350
    • Balas, E.1    Tama, J.2    Tind, J.3
  • 8
    • 38749116247 scopus 로고    scopus 로고
    • A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations
    • DOI 10.1007/s10107-006-0080-6
    • S. Burer D. Vandenbussche 2008 A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations Math. Program. 113 3 259 282 1135.90034 10.1007/s10107-006-0080-6 2375483 (Pubitemid 351177972)
    • (2008) Mathematical Programming , vol.113 , Issue.2 , pp. 259-282
    • Burer, S.1    Vandenbussche, D.2
  • 9
    • 33846858656 scopus 로고    scopus 로고
    • Revival of the Gomory cuts in the 1990's
    • 10.1007/s10479-006-0100-1 2313362
    • G. Cornuéjols 2007 Revival of the Gomory cuts in the 1990's Ann. Oper. Res. 149 1 63 66 10.1007/s10479-006-0100-1 2313362
    • (2007) Ann. Oper. Res. , vol.149 , Issue.1 , pp. 63-66
    • Cornuéjols, G.1
  • 10
    • 34250080270 scopus 로고
    • Laplacian eigenvalues and the maximum cut problem
    • 10.1007/BF01585184 1251892
    • C. Delorme S. Poljak 1993 Laplacian eigenvalues and the maximum cut problem Math. Program. Ser. A 62 3 557 574 10.1007/BF01585184 1251892
    • (1993) Math. Program. Ser. A , vol.62 , Issue.3 , pp. 557-574
    • Delorme, C.1    Poljak, S.2
  • 11
    • 33947096119 scopus 로고    scopus 로고
    • Optimizing over the first Chvátal closure
    • DOI 10.1007/s10107-006-0054-8
    • M. Fischetti A. Lodi 2007 Optimizing over the first Chvátal closure Math. Program. 110 1 3 20 05145050 10.1007/s10107-006-0054-8 2306128 (Pubitemid 46411827)
    • (2007) Mathematical Programming , vol.110 , Issue.1 , pp. 3-20
    • Fischetti, M.1    Lodi, A.2
  • 13
    • 77955171009 scopus 로고    scopus 로고
    • GLOBALLib
    • GLOBALLib, www.gamsworld.org/global/globallib/globalstat.htm
  • 14
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • 0885.68088 10.1145/227683.227684 1412228
    • M.X. Goemans D.P. Williamson 1995 Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming J. ACM 42 6 1115 1145 0885.68088 10.1145/227683.227684 1412228
    • (1995) J. ACM , vol.42 , Issue.6 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 16
    • 0011778875 scopus 로고
    • There cannot be any algorithm for integer programming with quadratic constraints
    • 0257.90029 10.1287/opre.21.1.221 354007
    • R.G. Jeroslow 1973 There cannot be any algorithm for integer programming with quadratic constraints Oper. Res. 21 1 221 224 0257.90029 10.1287/opre.21.1.221 354007
    • (1973) Oper. Res. , vol.21 , Issue.1 , pp. 221-224
    • Jeroslow, R.G.1
  • 17
    • 0036455609 scopus 로고    scopus 로고
    • Second order cone programming relaxation of nonconvex quadratic optimization problems
    • 1109.90327 10.1080/10556780108805819 1892585
    • S. Kim M. Kojima 2001 Second order cone programming relaxation of nonconvex quadratic optimization problems Optim. Methods Softw. 15 201 204 1109.90327 10.1080/10556780108805819 1892585
    • (2001) Optim. Methods Softw. , vol.15 , pp. 201-204
    • Kim, S.1    Kojima, M.2
  • 18
    • 4243480492 scopus 로고
    • On a positive semidefinite relaxation of the cut polytope. Special issue honoring Miroslav Fiedler and Vlastimil Ptk
    • 10.1016/0024-3795(95)00271-R 1340705
    • M. Laurent S. Poljak 1995 On a positive semidefinite relaxation of the cut polytope. Special issue honoring Miroslav Fiedler and Vlastimil Ptk Linear Algebra Appl. 223/224 439 461 10.1016/0024-3795(95)00271-R 1340705
    • (1995) Linear Algebra Appl. , vol.223-224 , pp. 439-461
    • Laurent, M.1    Poljak, S.2
  • 19
    • 0030499632 scopus 로고    scopus 로고
    • On the facial structure of the set of correlation matrices
    • 0855.15011 10.1137/0617031 1397243
    • M. Laurent S. Poljak 1996 On the facial structure of the set of correlation matrices SIAM J. Matrix Anal. Appl. 17 3 530 547 0855.15011 10.1137/0617031 1397243
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.3 , pp. 530-547
    • Laurent, M.1    Poljak, S.2
  • 20
    • 0035891492 scopus 로고    scopus 로고
    • A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems
    • 10.1016/S0098-1354(01)00732-3
    • S. Lee I.E. Grossmann 2001 A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems Comput. Chem. Eng. 25 1675 1697 10.1016/S0098-1354(01)00732-3
    • (2001) Comput. Chem. Eng. , vol.25 , pp. 1675-1697
    • Lee, S.1    Grossmann, I.E.2
  • 21
    • 0000108196 scopus 로고    scopus 로고
    • NP-hardness of linear multiplicative programming and related problems
    • 0868.90111 10.1007/BF00121658 1411603
    • T. Matsui 1996 NP-hardness of linear multiplicative programming and related problems J. Glob. Optim. 9 113 119 0868.90111 10.1007/BF00121658 1411603
    • (1996) J. Glob. Optim. , vol.9 , pp. 113-119
    • Matsui, T.1
  • 22
    • 34250381644 scopus 로고
    • Computability of global solutions to factorable nonconvex programs: Part i Convex underestimating problems
    • 0349.90100 10.1007/BF01580665 469281
    • G.P. McCormick 1976 Computability of global solutions to factorable nonconvex programs: part I Convex underestimating problems Math. Program. 10 1 147 175 0349.90100 10.1007/BF01580665 469281
    • (1976) Math. Program. , vol.10 , Issue.1 , pp. 147-175
    • McCormick, G.P.1
  • 23
    • 77955170794 scopus 로고    scopus 로고
    • PENNON
    • PENNON, http://www.penopt.com
  • 25
    • 80051591539 scopus 로고    scopus 로고
    • Convex relaxations of mixed integer quadratically constrained programs: Extended formulations
    • 08/2008. Available on Optimization Online
    • Saxena, A., Bonami, P., Lee, J.: Convex relaxations of mixed integer quadratically constrained programs: extended formulations. IBM Research Report RC24621, 08/2008. Available on Optimization Online
    • IBM Research Report RC24621
    • Saxena, A.1    Bonami, P.2    Lee, J.3
  • 26
    • 80051591539 scopus 로고    scopus 로고
    • Convex relaxations of mixed integer quadratically constrained programs: Projected formulations
    • 11/2008. Available on Optimization Online
    • Saxena, A., Bonami, P., Lee, J.: Convex relaxations of mixed integer quadratically constrained programs: projected formulations. IBM Research Report RC24695, 11/2008. Available on Optimization Online
    • IBM Research Report RC24695
    • Saxena, A.1    Bonami, P.2    Lee, J.3
  • 27
    • 67349234083 scopus 로고    scopus 로고
    • MIP reformulations of the probabilistic set covering problem
    • to appear
    • Saxena, A., Goyal, V., Lejeune, M.: MIP reformulations of the probabilistic set covering problem. Math. Program. (to appear)
    • Math. Program.
    • Saxena, A.1    Goyal, V.2    Lejeune, M.3
  • 28
    • 38249015247 scopus 로고
    • Relaxations for probabilistically constrained programs with discrete random variables
    • 0765.90071 10.1016/0167-6377(92)90037-4 1167427
    • S. Sen 1992 Relaxations for probabilistically constrained programs with discrete random variables Oper. Res. Lett. 11 2 81 86 0765.90071 10.1016/0167-6377(92)90037-4 1167427
    • (1992) Oper. Res. Lett. , vol.11 , Issue.2 , pp. 81-86
    • Sen, S.1
  • 30
    • 33745955604 scopus 로고    scopus 로고
    • Enhancing RLT relaxations via a new class of semidefinite cuts
    • 1045.90044 10.1023/A:1013819515732 1878144
    • H.D. Sherali B.M.P. Fraticelli 2002 Enhancing RLT relaxations via a new class of semidefinite cuts J. Glob. Optim. 22 233 261 1045.90044 10.1023/A:1013819515732 1878144
    • (2002) J. Glob. Optim. , vol.22 , pp. 233-261
    • Sherali, H.D.1    Fraticelli, B.M.P.2
  • 31
    • 0001367989 scopus 로고    scopus 로고
    • A branch-and-cut method for 0-1 mixed convex programming
    • 0946.90054 10.1007/s101070050103 1733745
    • R. Stubbs S. Mehrotra 1999 A branch-and-cut method for 0-1 mixed convex programming Math. Program. 86 515 532 0946.90054 10.1007/s101070050103 1733745
    • (1999) Math. Program. , vol.86 , pp. 515-532
    • Stubbs, R.1    Mehrotra, S.2
  • 32
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • 10.1080/10556789908805766 1778433
    • J.F. Sturm 1999 Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optim. Methods Softw. 11-12 625 653 10.1080/10556789908805766 1778433
    • (1999) Optim. Methods Softw. , vol.1112 , pp. 625-653
    • Sturm, J.F.1
  • 34
    • 2942665751 scopus 로고    scopus 로고
    • Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
    • DOI 10.1007/s10107-003-0467-6
    • M. Tawarmalani N.V. Sahinidis 2004 Global optimization of mixed integer nonlinear programs: A theoretical and computational study Math. Program. 99 3 563 591 1062.90041 10.1007/s10107-003-0467-6 2051712 (Pubitemid 40871718)
    • (2004) Mathematical Programming , vol.99 , Issue.3 , pp. 563-591
    • Tawarmalani, M.1    Sahinidis, N.V.2
  • 35
    • 17444372087 scopus 로고    scopus 로고
    • A polyhedral study of nonconvex quadratic programs with box constraints
    • DOI 10.1007/s10107-004-0549-0
    • D. Vandenbussche G.L. Nemhauser 2005 A polyhedral study of nonconvex quadratic programs with box constraints Math. Program. 102 3 531 557 1137.90009 10.1007/s10107-004-0549-0 2136226 (Pubitemid 40536653)
    • (2005) Mathematical Programming , vol.102 , Issue.3 , pp. 531-557
    • Vandenbussche, D.1    Nemhauser, G.L.2
  • 36
    • 17444382397 scopus 로고    scopus 로고
    • A branch-and-cut algorithm for nonconvex quadratic programs with box constraints
    • DOI 10.1007/s10107-004-0550-7
    • D. Vandenbussche G.L. Nemhauser 2005 A branch-and-cut algorithm for nonconvex quadratic programs with box constraints Math. Program. 102 3 559 575 1137.90010 10.1007/s10107-004-0550-7 2136227 (Pubitemid 40536654)
    • (2005) Mathematical Programming , vol.102 , Issue.3 , pp. 559-575
    • Vandenbussche, D.1    Nemhauser, G.L.2
  • 37
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
    • DOI 10.1007/s10107-004-0559-y
    • A. Wächter L.T. Biegler 2006 On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming Math. Program. 106 1 25 57 1134.90542 10.1007/s10107-004-0559-y 2195616 (Pubitemid 41813168)
    • (2006) Mathematical Programming , vol.106 , Issue.1 , pp. 25-57
    • Wachter, A.1    Biegler, L.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.