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Volumn 15, Issue 3, 2005, Pages 697-719

Generalized lagrangian duals and sums of squares relaxations of sparse polynomial optimization blems

Author keywords

Global optimization; Lagrangian dual; Lagrangian relaxation; Polynomial optimization problem; Semidefinite program; Semidefinite program relaxation; Sparsity; Sums of squares optimization

Indexed keywords

APPROXIMATION THEORY; HEURISTIC METHODS; INTEGER PROGRAMMING; LAGRANGE MULTIPLIERS; NUMERICAL ANALYSIS; POLYNOMIALS;

EID: 23844439934     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/030601260     Document Type: Article
Times cited : (50)

References (21)
  • 1
    • 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. Program., 58 (1993), pp. 295-323.
    • (1993) Math. Program. , vol.58 , pp. 295-323
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 2
    • 0000082954 scopus 로고
    • Sums of squares of real polynomials
    • k-theory and Algebra Geometry: Connections with Quadratic Forms and Division Algebras, AMS, Providence RI
    • M. D. CHOI, T. Y. LAM, AND B. REZNICK, Sums of squares of real polynomials, in k-theory and Algebra Geometry: Connections with Quadratic Forms and Division Algebras, Proc. Sympos. Pure Math, 58 Part 2, AMS, Providence RI, 1995, pp. 103-126.
    • (1995) Proc. Sympos. Pure Math , vol.58 , Issue.2 PART , pp. 103-126
    • Choi, M.D.1    Lam, T.Y.2    Reznick, B.3
  • 3
    • 2542587541 scopus 로고    scopus 로고
    • GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
    • D. HENRION AND J. B. LASSERRE, GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi, ACM Trans. Math. Software, 29 (2003), pp. 165-194.
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 165-194
    • Henrion, D.1    Lasserre, J.B.2
  • 4
    • 0036455609 scopus 로고    scopus 로고
    • Second order cone programming relaxation of nonconvex quadratic optimization problems
    • S. KIM AND M. KOJIMA, Second order cone programming relaxation of nonconvex quadratic optimization problems, Optim. Method Softw., 15 (2001), pp. 201-224.
    • (2001) Optim. Method Softw. , vol.15 , pp. 201-224
    • Kim, S.1    Kojima, M.2
  • 5
    • 0242302674 scopus 로고    scopus 로고
    • Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations
    • S. KIM AND M. KOJIMA, Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations, Comput. Optim. Appl., 26 (2003), pp. 143-154.
    • (2003) Comput. Optim. Appl. , vol.26 , pp. 143-154
    • Kim, S.1    Kojima, M.2
  • 6
    • 0242592654 scopus 로고    scopus 로고
    • A general framework for convex relaxation of polynomial optimization problems over cones
    • M. KOJIMA, S. KIM, AND H. WAKI, A general framework for convex relaxation of polynomial optimization problems over cones, J. Oper. Res. Soc. Japan, 46 (2003), pp. 125-144.
    • (2003) J. Oper. Res. Soc. Japan , vol.46 , pp. 125-144
    • Kojima, M.1    Kim, S.2    Waki, H.3
  • 7
    • 33645266917 scopus 로고    scopus 로고
    • Sparsity in sums of squares of polynomials
    • Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo
    • M. KOJIMA, S. KIM, AND H. WAKI, Sparsity in Sums of Squares of Polynomials, Research Report B-391, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 2003.
    • (2003) Research Report , vol.B-391
    • Kojima, M.1    Kim, S.2    Waki, H.3
  • 8
    • 0040214558 scopus 로고    scopus 로고
    • Cones of matrices and successive convex relaxations of nonconvex sets
    • M. KOJIMA AND L. TUNÇEL, Cones of matrices and successive convex relaxations of nonconvex sets, SIAM J. Optim., 10 (2000), pp. 750-778.
    • (2000) SIAM J. Optim. , vol.10 , pp. 750-778
    • Kojima, M.1    Tunçel, L.2
  • 9
    • 31844438920 scopus 로고    scopus 로고
    • Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems
    • M. KOJIMA AND L. TUNÇEL, Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems, Math. Program., 89 (2000), pp. 79-111.
    • (2000) Math. Program. , vol.89 , pp. 79-111
    • Kojima, M.1    Tunçel, L.2
  • 10
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • J. B. LASSERRE, Global optimization with polynomials and the problem of moments, SIAM J. Optim., 11 (2001), pp. 796-817.
    • (2001) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 11
    • 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
  • 12
    • 21644433736 scopus 로고    scopus 로고
    • First- and second-order methods for semidefinite programming
    • R. D. C. MONTEIRO, First- and second-order methods for semidefinite programming, Math. Program., 97 (2003), pp. 209-244.
    • (2003) Math. Program. , vol.97 , pp. 209-244
    • Monteiro, R.D.C.1
  • 13
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • P. A. PARRILO, Semidefinite programming relaxations for semialgebraic problems, Math. Program., 96 (2003), pp. 293-320.
    • (2003) Math. Program. , vol.96 , pp. 293-320
    • Parrilo, P.A.1
  • 15
    • 0032064831 scopus 로고    scopus 로고
    • An algorithm for sums of squares of real polynomials
    • V. POWERS AND T. WÖRMANN, An algorithm for sums of squares of real polynomials, J. Pure Appl. Algebra, 127 (1998), pp. 99-104.
    • (1998) J. Pure Appl. Algebra , vol.127 , pp. 99-104
    • Powers, V.1    Wörmann, T.2
  • 16
    • 0000135301 scopus 로고
    • Positive polynomials on compact semi-algebraic sets
    • M. PUTINAR, Positive polynomials on compact semi-algebraic sets, Indiana U. Math. J., 42 (1993), pp. 969-984.
    • (1993) Indiana U. Math. J. , vol.42 , pp. 969-984
    • Putinar, M.1
  • 17
    • 84972566433 scopus 로고
    • Extremal psd forms with few terms
    • B. REZNICK, Extremal psd forms with few terms, Duke Math. J., 45 (1978), pp. 363-374.
    • (1978) Duke Math. J. , vol.45 , pp. 363-374
    • Reznick, B.1
  • 18
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • H. D. SHERALI AND W. P. ADAMS, A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems, SIAM J. Discrete Math., 3 (1990), pp. 411-430.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 411-430
    • Sherali, H.D.1    Adams, W.P.2
  • 19
    • 0001642333 scopus 로고
    • A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique
    • H. D. SHERALI AND C. H. TUNCBILEK, A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique, J. Global Optim., 2 (1992), pp. 101-112.
    • (1992) J. Global Optim. , vol.2 , pp. 101-112
    • Sherali, H.D.1    Tuncbilek, C.H.2
  • 20
    • 0002500749 scopus 로고
    • A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems
    • H. D. SHERALI AND W. P. ADAMS, A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems, Discrete Appl. Math., 52 (1994), pp. 83-106.
    • (1994) Discrete Appl. Math. , vol.52 , pp. 83-106
    • Sherali, H.D.1    Adams, W.P.2
  • 21
    • 0042486152 scopus 로고    scopus 로고
    • Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0)
    • M. YAMASHITA, K. FUJISAWA, AND M. KOJIMA, Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0), Optim. Method Softw., 18 (2003), pp. 491-505.
    • (2003) Optim. Method Softw. , vol.18 , pp. 491-505
    • Yamashita, M.1    Fujisawa, K.2    Kojima, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.