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Volumn 15, Issue 4, 2008, Pages 767-801

Set-semidefinite optimization

Author keywords

Convex analysis; Copositive programming; Semidefinite programming; Vector optimization

Indexed keywords


EID: 59649110020     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (41)

References (53)
  • 1
    • 21844502368 scopus 로고
    • Criteria for copositive matrices using simplices and barycentric coordinates
    • L.-F. Andersson, G. Chang, T. Elfving: Criteria for copositive matrices using simplices and barycentric coordinates, Linear Algebra Appl. 220 (1995) 9-30.
    • (1995) Linear Algebra Appl , vol.220 , pp. 9-30
    • Andersson, L.-F.1    Chang, G.2    Elfving, T.3
  • 3
    • 0000034358 scopus 로고
    • From optimization and variational inequalities to equilibrium problems
    • E. Blum, W. Oettli: From optimization and variational inequalities to equilibrium problems, Math. Stud. 63 (1994) 123-145.
    • (1994) Math. Stud , vol.63 , pp. 123-145
    • Blum, E.1    Oettli, W.2
  • 4
    • 0034342188 scopus 로고    scopus 로고
    • Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality
    • I. M. Bomze: Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality, SIAM J. Matrix Anal. Appl. 21 (2000) 840-848.
    • (2000) SIAM J. Matrix Anal. Appl , vol.21 , pp. 840-848
    • Bomze, I.M.1
  • 5
    • 31244435061 scopus 로고    scopus 로고
    • Solving standard quadratic optimization problems via linear, semidefinite and copositive programming
    • I. M. Bomze, E. de Klerk: Solving standard quadratic optimization problems via linear, semidefinite and copositive programming, J. Glob. Optim. 24 (2002) 163-185.
    • (2002) J. Glob. Optim , vol.24 , pp. 163-185
    • Bomze, I.M.1    de Klerk, E.2
  • 8
    • 0020305083 scopus 로고
    • Necessary and sufficient conditions for quadratic minimality
    • J. M. Borwein: Necessary and sufficient conditions for quadratic minimality, Numer. Funct. Anal. Optimization 5 (1982) 127-140.
    • (1982) Numer. Funct. Anal. Optimization , vol.5 , pp. 127-140
    • Borwein, J.M.1
  • 10
    • 38849167450 scopus 로고    scopus 로고
    • Algorithmic copositivity detection by simplicial partition
    • S. Bundfuss, M. Dür: Algorithmic copositivity detection by simplicial partition, Linear Algebra Appl. 428 (2008) 1511-1523.
    • (2008) Linear Algebra Appl , vol.428 , pp. 1511-1523
    • Bundfuss, S.1    Dür, M.2
  • 11
    • 59649090658 scopus 로고    scopus 로고
    • S. Burer: On the copositive representation of binary and continuous nonconvex quadratic programs, Working paper, Department of Management Sciences, University of Iowa, Iowa City (2007).
    • S. Burer: On the copositive representation of binary and continuous nonconvex quadratic programs, Working paper, Department of Management Sciences, University of Iowa, Iowa City (2007).
  • 14
    • 0026970916 scopus 로고
    • Role of copositivity in optimality criteria for nonconvex optimization problems
    • G. Danninger: Role of copositivity in optimality criteria for nonconvex optimization problems, J. Optimization Theory Appl. 75 (1992) 535-558.
    • (1992) J. Optimization Theory Appl , vol.75 , pp. 535-558
    • Danninger, G.1
  • 15
    • 34250084013 scopus 로고
    • Using copositivity for global optimality criteria in concave quadratic programming problems
    • G. Danninger, I. M. Bomze: Using copositivity for global optimality criteria in concave quadratic programming problems, Math. Program. 62 (1993) 575-580.
    • (1993) Math. Program , vol.62 , pp. 575-580
    • Danninger, G.1    Bomze, I.M.2
  • 16
    • 33646724947 scopus 로고    scopus 로고
    • On the equivalence of algebraic approaches to the minimization of forms on the simplex
    • Positive Polynomials in Control, D. Henrion, A. Garulli eds, Springer, Berlin
    • E. de Klerk, M. Laurent, P. Parrillo: On the equivalence of algebraic approaches to the minimization of forms on the simplex, in: Positive Polynomials in Control, D. Henrion, A. Garulli (eds.), Lecture Notes in Control and Information Sciences 312, Springer, Berlin (2005) 121-132.
    • (2005) Lecture Notes in Control and Information Sciences , vol.312 , pp. 121-132
    • de Klerk, E.1    Laurent, M.2    Parrillo, P.3
  • 17
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • E. de Klerk, D. V. Pasechnik: Approximation of the stability number of a graph via copositive programming, SIAM J. Optim. 12 (2002) 875-892.
    • (2002) SIAM J. Optim , vol.12 , pp. 875-892
    • de Klerk, E.1    Pasechnik, D.V.2
  • 18
    • 59649104373 scopus 로고    scopus 로고
    • Computational prospects on copositive programming
    • M. Fukuda, M. Yamashita, M. Kojima: Computational prospects on copositive programming, RIMS Kokyuroku 1526 (2006) 207-213.
    • (2006) RIMS Kokyuroku , vol.1526 , pp. 207-213
    • Fukuda, M.1    Yamashita, M.2    Kojima, M.3
  • 19
    • 0022676744 scopus 로고
    • A characterization of positive semidefinite operators on a Hubert space
    • M. S. Gowda: A characterization of positive semidefinite operators on a Hubert space, J. Optimization Theory Appl. 48 (1986) 419-425.
    • (1986) J. Optimization Theory Appl , vol.48 , pp. 419-425
    • Gowda, M.S.1
  • 20
    • 0024705755 scopus 로고
    • Complementarity problems over locally compact cones
    • M. S. Gowda: Complementarity problems over locally compact cones, SIAM J. Control Optimization 27 (1989) 836-841.
    • (1989) SIAM J. Control Optimization , vol.27 , pp. 836-841
    • Gowda, M.S.1
  • 21
    • 0003258511 scopus 로고
    • On copositive matrices
    • K. P. Hadeler: On copositive matrices, Linear Algebra Appl. 49 (1983) 79-89.
    • (1983) Linear Algebra Appl , vol.49 , pp. 79-89
    • Hadeler, K.P.1
  • 22
    • 59649105657 scopus 로고
    • A conjugate decomposition of the Euclidean space
    • S.-P. Han, O. L. Mangasarian: A conjugate decomposition of the Euclidean space, Proc. Natl. Acad. Sci. USA 80 (1983) 5156-5157.
    • (1983) Proc. Natl. Acad. Sci. USA , vol.80 , pp. 5156-5157
    • Han, S.-P.1    Mangasarian, O.L.2
  • 23
    • 48749139631 scopus 로고
    • Conjugate cone characterization of positive definite and semidefinite matrices
    • S.-P. Han, O. L. Mangasarian: Conjugate cone characterization of positive definite and semidefinite matrices, Linear Algebra Appl. 56 (1984) 89-103.
    • (1984) Linear Algebra Appl , vol.56 , pp. 89-103
    • Han, S.-P.1    Mangasarian, O.L.2
  • 24
    • 0041904419 scopus 로고
    • Approximation by matrices positive semidefinite on a subspace
    • T. L. Hayden, J. Wells: Approximation by matrices positive semidefinite on a subspace, Linear Algebra Appl. 109 (1988) 115-130.
    • (1988) Linear Algebra Appl , vol.109 , pp. 115-130
    • Hayden, T.L.1    Wells, J.2
  • 26
    • 10444271520 scopus 로고    scopus 로고
    • Conditionally definite matrices
    • New York
    • K. D. Ikramov, N. V. Savel'eva: Conditionally definite matrices, J. Math. Sci., New York 98 (2000) 1-50.
    • (2000) J. Math. Sci , vol.98 , pp. 1-50
    • Ikramov, K.D.1    Savel'eva, N.V.2
  • 30
    • 0034383022 scopus 로고    scopus 로고
    • A test for copositive matrices
    • W. Kaplan: A test for copositive matrices, Linear Algebra Appl. 313 (2000) 203-206.
    • (2000) Linear Algebra Appl , vol.313 , pp. 203-206
    • Kaplan, W.1
  • 31
    • 0035501550 scopus 로고    scopus 로고
    • A copositivity probe
    • W. Kaplan: A copositivity probe, Linear Algebra Appl. 337 (2001) 237-251.
    • (2001) Linear Algebra Appl , vol.337 , pp. 237-251
    • Kaplan, W.1
  • 32
    • 34249955524 scopus 로고
    • Strictly copositive matrices and ESS's
    • H. Länger: Strictly copositive matrices and ESS's, Arch. Math. 55 (1990) 516-520.
    • (1990) Arch. Math , vol.55 , pp. 516-520
    • Länger, H.1
  • 33
    • 0016470698 scopus 로고
    • Positive operators on the n-dimensional ice cream cone
    • R. Loewy, H. Schneider: Positive operators on the n-dimensional ice cream cone, J. Math. Anal. Appl. 49 (1975) 375-392.
    • (1975) J. Math. Anal. Appl , vol.49 , pp. 375-392
    • Loewy, R.1    Schneider, H.2
  • 34
    • 34250967722 scopus 로고
    • Über monotone Matrixfunktionen
    • K. Löwner: Über monotone Matrixfunktionen, Math. Z. 38 (1934) 177-216.
    • (1934) Math. Z , vol.38 , pp. 177-216
    • Löwner, K.1
  • 35
    • 59649118608 scopus 로고
    • Conditional positivity of quadratic forms in Hilbert space
    • D. H. Martin: Conditional positivity of quadratic forms in Hilbert space, SIAM J. Math. Anal. 11 (1980) 1047-1057.
    • (1980) SIAM J. Math. Anal , vol.11 , pp. 1047-1057
    • Martin, D.H.1
  • 36
    • 3042895560 scopus 로고
    • Finite criteria for conditional definiteness of quadratic forms
    • D. H. Martin: Finite criteria for conditional definiteness of quadratic forms, Linear Algebra Appl. 39 (1981) 9-21.
    • (1981) Linear Algebra Appl , vol.39 , pp. 9-21
    • Martin, D.H.1
  • 37
    • 0002958234 scopus 로고
    • First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
    • H. Maurer, J. Zowe: First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Program. 16 (1979) 98-110.
    • (1979) Math. Program , vol.16 , pp. 98-110
    • Maurer, H.1    Zowe, J.2
  • 39
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and linear programming
    • K. G. Murty, S. N. Kabadi: Some NP-complete problems in quadratic and linear programming, Math. Program. 39 (1987) 117-129.
    • (1987) Math. Program , vol.39 , pp. 117-129
    • Murty, K.G.1    Kabadi, S.N.2
  • 40
    • 59649107176 scopus 로고    scopus 로고
    • Structured Semidefinite Programs and Semi-Algebraic Geometry Methods in Robustness and Optimization, PhD Thesis, California Institute of Technology, Pasadena
    • P. A. Parrillo: Structured Semidefinite Programs and Semi-Algebraic Geometry Methods in Robustness and Optimization, PhD Thesis, California Institute of Technology, Pasadena (2000).
    • (2000)
    • Parrillo, P.A.1
  • 41
    • 59649090898 scopus 로고    scopus 로고
    • Application of Semidefinite and Copositive Programming in Combinatorial Optimization, PhD Thesis, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana
    • J. Povh: Application of Semidefinite and Copositive Programming in Combinatorial Optimization, PhD Thesis, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana (2006).
    • (2006)
    • Povh, J.1
  • 43
    • 39449117440 scopus 로고    scopus 로고
    • A copositive programming approach to graph partitioning
    • J. Povh, F. Rendl: A copositive programming approach to graph partitioning, SIAM J. Optim. 18 (2007) 223-241.
    • (2007) SIAM J. Optim , vol.18 , pp. 223-241
    • Povh, J.1    Rendl, F.2
  • 46
    • 0020905805 scopus 로고
    • On copositive matrices and strong ellipticity for isotropic elastic materials
    • H. C. Simpson, S. J. Spector: On copositive matrices and strong ellipticity for isotropic elastic materials, Arch. Ration. Mech. Anal. 84 (1983) 55-68.
    • (1983) Arch. Ration. Mech. Anal , vol.84 , pp. 55-68
    • Simpson, H.C.1    Spector, S.J.2
  • 47
    • 0038386380 scopus 로고    scopus 로고
    • On cones of nonnegative quadratic functions
    • J. F. Sturm, S. Zhang: On cones of nonnegative quadratic functions, Math. Oper. Res. 28 (2003) 246-267.
    • (2003) Math. Oper. Res , vol.28 , pp. 246-267
    • Sturm, J.F.1    Zhang, S.2
  • 48
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe, S. Boyd: Semidefinite programming, SIAM Rev. 38 (1996) 49-95.
    • (1996) SIAM Rev , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 49
    • 0003395487 scopus 로고    scopus 로고
    • H. Wolkowicz, R. Saigal, L. Vandenberghe eds, Kluwer, Dordrecht
    • H. Wolkowicz, R. Saigal, L. Vandenberghe (eds.): Handbook on Semidefinite Programming, Kluwer, Dordrecht (2000).
    • (2000) Handbook on Semidefinite Programming
  • 50
    • 0002126665 scopus 로고
    • Criteria for copositive matrices
    • H. Väliaho: Criteria for copositive matrices, Linear Algebra Appl. 81 (1986) 19-34.
    • (1986) Linear Algebra Appl , vol.81 , pp. 19-34
    • Väliaho, H.1
  • 51
    • 0010359916 scopus 로고
    • Testing the definiteness of matrices on polyhedral cones
    • H. Väliaho: Testing the definiteness of matrices on polyhedral cones, Linear Algebra Appl. 101 (1988) 136-165.
    • (1988) Linear Algebra Appl , vol.101 , pp. 136-165
    • Väliaho, H.1
  • 52
    • 0042092622 scopus 로고
    • Quadratic-programming criteria for copositive matrices
    • H. Väliaho: Quadratic-programming criteria for copositive matrices, Linear Algebra Appl. 119 (1989) 163-182.
    • (1989) Linear Algebra Appl , vol.119 , pp. 163-182
    • Väliaho, H.1


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