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Volumn 138, Issue 1-2, 2013, Pages 365-400

Copositivity detection by difference-of-convex decomposition and ω-subdivision

Author keywords

Conic optimization; Linear optimization; Quadratic optimization

Indexed keywords

BRANCH-AND-BOUND ALGORITHMS; CONIC OPTIMIZATION; D.C. DECOMPOSITION; LINEAR OPTIMIZATION; QUADRATIC OPTIMIZATION; TEST POINTS;

EID: 84875414878     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-012-0543-x     Document Type: Article
Times cited : (22)

References (43)
  • 1
    • 21844502368 scopus 로고
    • Criteria for copositive matrices using simplices and barycentric coordinates
    • 1334568 0826.15016 10.1016/0024-3795(94)00161-6
    • Andersson L.E.; Chang G.; Elfving T.: Criteria for copositive matrices using simplices and barycentric coordinates. Linear Algebra Appl. 220, 9-30 (1995)
    • (1995) Linear Algebra Appl. , vol.220 , pp. 9-30
    • Andersson, L.E.1    Chang, G.2    Elfving, T.3
  • 2
    • 0001811674 scopus 로고
    • Copositivity conditions for global optimality in indefinite quadratic programming problems
    • 0972.90051
    • Bomze I.M.: Copositivity conditions for global optimality in indefinite quadratic programming problems. Czechoslov. J. Oper. Res. 1, 7-19 (1992)
    • (1992) Czechoslov. J. Oper. Res. , vol.1 , pp. 7-19
    • Bomze, I.M.1
  • 3
    • 0030486436 scopus 로고    scopus 로고
    • Block pivoting and shortcut strategies for detecting copositivity
    • 1416455 0862.65036 10.1016/0024-3795(95)00165-4
    • Bomze I.M.: Block pivoting and shortcut strategies for detecting copositivity. Linear Algebra Appl. 248, 161-184 (1996)
    • (1996) Linear Algebra Appl. , vol.248 , pp. 161-184
    • Bomze, I.M.1
  • 4
    • 0041858636 scopus 로고    scopus 로고
    • Global escape strategies for maximizing quadratic forms over a simplex
    • 1469131 0904.90125 10.1023/A:1008297330705
    • Bomze I.M.: Global escape strategies for maximizing quadratic forms over a simplex. J. Glob. Optim. 11, 325-338 (1997)
    • (1997) J. Glob. Optim. , vol.11 , pp. 325-338
    • Bomze, I.M.1
  • 5
    • 0000462690 scopus 로고    scopus 로고
    • On standard quadratic optimization problems
    • 1673454 0916.90214 10.1023/A:1008369322970
    • Bomze I.M.: On standard quadratic optimization problems. J. Glob. Optim. 13, 369-387 (1998)
    • (1998) J. Glob. Optim. , vol.13 , pp. 369-387
    • Bomze, I.M.1
  • 6
    • 0034342188 scopus 로고    scopus 로고
    • Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality
    • 1740875 0953.65028 10.1137/S0895479898341487
    • Bomze I.M.: Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality. SIAM J. Matrix Anal. Appl. 21, 840-848 (2000)
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 840-848
    • Bomze, I.M.1
  • 7
    • 42749096246 scopus 로고    scopus 로고
    • Perron-Frobenius property of copositive matrices, and a block copositivity criterion
    • 2419140 1154.15308 10.1016/j.laa.2008.02.003
    • Bomze I.M.: Perron-Frobenius property of copositive matrices, and a block copositivity criterion. Linear Algebra Appl. 429, 68-71 (2008)
    • (2008) Linear Algebra Appl. , vol.429 , pp. 68-71
    • Bomze, I.M.1
  • 8
    • 80053917198 scopus 로고    scopus 로고
    • Copositive optimization - Recent developments and applications
    • 2845851 06035164 10.1016/j.ejor.2011.04.026
    • Bomze I.M.: Copositive optimization - recent developments and applications. Eur. J. Oper. Res. 216, 509-520 (2012)
    • (2012) Eur. J. Oper. Res. , vol.216 , pp. 509-520
    • Bomze, I.M.1
  • 10
    • 0000462690 scopus 로고    scopus 로고
    • On copositive programming and standard quadratic optimization problems
    • 0916.90214 10.1023/A:1008369322970
    • Bomze I.M.; Dür M.; de Klerk E.; Roos C.; Quist A.J.; Terlaky T.: On copositive programming and standard quadratic optimization problems. J. Glob. Optim. 13, 369-387 (1998)
    • (1998) J. Glob. Optim. , vol.13 , pp. 369-387
    • Bomze, I.M.1    Dür, M.2    De Klerk, E.3    Roos, C.4    Quist, A.J.5    Terlaky, T.6
  • 11
    • 3543079910 scopus 로고    scopus 로고
    • Undominated d.c. decompositions of quadratic functions and applications to branch-and-bound approaches
    • 2072534 1056.90112 10.1023/B:COAP.0000026886.61324.e4
    • Bomze I.M.; Locatelli M.: Undominated d.c. decompositions of quadratic functions and applications to branch-and-bound approaches. Comput. Optim. Appl. 28, 227-245 (2004)
    • (2004) Comput. Optim. Appl. , vol.28 , pp. 227-245
    • Bomze, I.M.1    Locatelli, M.2
  • 12
    • 43949093438 scopus 로고    scopus 로고
    • New and old bounds for standard quadratic optimization: Dominance, equivalence and incomparability
    • 2403752 1171.90007 10.1007/s10107-007-0138-0
    • Bomze I.M.; Locatelli M.; Tardella F.: New and old bounds for standard quadratic optimization: dominance, equivalence and incomparability. Math. Program. 115, 31-64 (2008)
    • (2008) Math. Program. , vol.115 , pp. 31-64
    • Bomze, I.M.1    Locatelli, M.2    Tardella, F.3
  • 13
    • 84859268096 scopus 로고    scopus 로고
    • Think co(mpletely)positive! Matrix properties, examples and a clustered bibliography on copositive optimization
    • 2892529 06046177 10.1007/s10898-011-9749-3
    • Bomze I.M.; Schachinger W.; Uchida G.: Think co(mpletely)positive! Matrix properties, examples and a clustered bibliography on copositive optimization. J. Glob. Optim. 52, 423-445 (2012)
    • (2012) J. Glob. Optim. , vol.52 , pp. 423-445
    • Bomze, I.M.1    Schachinger, W.2    Uchida, G.3
  • 14
    • 38849167450 scopus 로고    scopus 로고
    • Algorithmic copositivity detection by simplicial partition
    • 2388635 1138.15007 10.1016/j.laa.2007.09.035
    • Bundfuss S.; Dür M.: Algorithmic copositivity detection by simplicial partition. Linear Algebra Appl. 428, 1511-1523 (2008)
    • (2008) Linear Algebra Appl. , vol.428 , pp. 1511-1523
    • Bundfuss, S.1    Dür, M.2
  • 15
    • 67349282710 scopus 로고    scopus 로고
    • On the copositive representation of binary and continuous nonconvex quadratic programs
    • 2505747 1180.90234 10.1007/s10107-008-0223-z
    • Burer S.: On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Program. 120, 479-495 (2009)
    • (2009) Math. Program. , vol.120 , pp. 479-495
    • Burer, S.1
  • 18
    • 34250084013 scopus 로고
    • Using copositivity for global optimality criteria in concave quadratic programming problems
    • 1251893 0803.90097 10.1007/BF01585185
    • Danninger G.; Bomze I.M.: Using copositivity for global optimality criteria in concave quadratic programming problems. Math. Program. 62, 575-580 (1993)
    • (1993) Math. Program. , vol.62 , pp. 575-580
    • Danninger, G.1    Bomze, I.M.2
  • 19
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • 1922500 1035.90058 10.1137/S1052623401383248
    • de Klerk E.; Pasechnik D.V.: Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12, 875-892 (2002)
    • (2002) SIAM J. Optim. , vol.12 , pp. 875-892
    • De Klerk, E.1    Pasechnik, D.V.2
  • 20
    • 0002106815 scopus 로고
    • On non-negative forms in real variables some or all of which are non-negative
    • 137686 0108.04803 10.1017/S0305004100036185
    • Diananda P.H.: On non-negative forms in real variables some or all of which are non-negative. Proc. Camb. Phil. Soc. 58, 17-25 (1962)
    • (1962) Proc. Camb. Phil. Soc. , vol.58 , pp. 17-25
    • Diananda, P.H.1
  • 21
    • 84875436629 scopus 로고    scopus 로고
    • Test instances Last accessed Jan 13.
    • DIMACS: Second DIMACS Challenge. Test instances available at http://dimacs.rutgers.edu/challenges. Last accessed Jan 13. (2010)
    • (2010) DIMACS: Second DIMACS Challenge
  • 23
    • 59649110020 scopus 로고    scopus 로고
    • Set-semidefinite optimization
    • 2489613 1172.90013
    • Eichfelder G.; Jahn J.: Set-semidefinite optimization. J. Convex Anal. 15, 767-801 (2008)
    • (2008) J. Convex Anal. , vol.15 , pp. 767-801
    • Eichfelder, G.1    Jahn, J.2
  • 24
    • 84976339091 scopus 로고    scopus 로고
    • Foundations of set-semidefinite optimization
    • Pardalos T.M. Rassias A.A. Khan (eds) Springer New York
    • Eichfelder G.; Jahn J.: Foundations of set-semidefinite optimization. In: Pardalos, P.; Rassias, T.M.; Khan, A.A (eds.) Nonlinear Analysis and Variational Problems, pp. 259-284. Springer, New York (2009)
    • (2009) Nonlinear Analysis and Variational Problems , pp. 259-284
    • Eichfelder, G.1    Jahn, J.2
  • 25
    • 0000606957 scopus 로고
    • Copositive and completely positive quadratic forms
    • 147484 0124.25302 10.1017/S0305004100036951
    • Hall M. Jr.; Newman M.: Copositive and completely positive quadratic forms. Proc. Camb. Phil. Soc. 59, 329-339 (1963)
    • (1963) Proc. Camb. Phil. Soc. , vol.59 , pp. 329-339
    • Hall, M.Jr.1    Newman, M.2
  • 27
    • 0041777617 scopus 로고
    • Two remarks on copositive matrices
    • 248157 0185.08004 10.1016/0024-3795(69)90011-1
    • Haynsworth E.; Hoffman A.J.: Two remarks on copositive matrices. Linear Algebra Appl. 2, 387-392 (1969)
    • (1969) Linear Algebra Appl. , vol.2 , pp. 387-392
    • Haynsworth, E.1    Hoffman, A.J.2
  • 28
    • 24344438575 scopus 로고    scopus 로고
    • The copositive completion problem
    • 2166863 1098.15010 10.1016/j.laa.2005.06.019
    • Hogben L.; Johnson C.R.; Reams R.: The copositive completion problem. Linear Algebra Appl. 408, 207-211 (2005)
    • (2005) Linear Algebra Appl. , vol.408 , pp. 207-211
    • Hogben, L.1    Johnson, C.R.2    Reams, R.3
  • 29
    • 10444244660 scopus 로고
    • On copositive matrices with -1, 0, 1 entries
    • 316482 0273.15019 10.1016/0097-3165(73)90006-X
    • Hoffman A.J.; Pereira F.: On copositive matrices with -1, 0, 1 entries. J. Comb. Theory (A) 14, 302-309 (1973)
    • (1973) J. Comb. Theory (A) , vol.14 , pp. 302-309
    • Hoffman, A.J.1    Pereira, F.2
  • 32
    • 0031513087 scopus 로고    scopus 로고
    • On generalized bisection of n-simplices
    • 1388889
    • Horst R.: On generalized bisection of n-simplices. Math. Comput. 218, 691-698 (1997)
    • (1997) Math. Comput. , vol.218 , pp. 691-698
    • Horst, R.1
  • 33
    • 0035501550 scopus 로고    scopus 로고
    • A copositivity probe
    • 1856859 0999.15027 10.1016/S0024-3795(01)00351-2
    • Kaplan W.: A copositivity probe. Linear Algebra Appl. 337, 237-251 (2001)
    • (2001) Linear Algebra Appl. , vol.337 , pp. 237-251
    • Kaplan, W.1
  • 34
    • 0034288769 scopus 로고    scopus 로고
    • On the convergence of the simplicial branch-and-bound algorithm based on ω-subdivisions
    • 1800929 0970.90062 10.1023/A:1004604732705
    • Locatelli M.; Raber U.: On the convergence of the simplicial branch-and-bound algorithm based on ω-subdivisions. J. Optim. Theor. Appl. 107, 69-79 (2000)
    • (2000) J. Optim. Theor. Appl. , vol.107 , pp. 69-79
    • Locatelli, M.1    Raber, U.2
  • 35
    • 0034349660 scopus 로고    scopus 로고
    • A finiteness result for the simplicial branch-and bound algorithm based on ω-subdivisions
    • 1800930 0970.90061 10.1023/A:1004656716776
    • Locatelli M.; Raber U.: A finiteness result for the simplicial branch-and bound algorithm based on ω-subdivisions. J. Optim. Theor. Appl. 107, 81-88 (2000)
    • (2000) J. Optim. Theor. Appl. , vol.107 , pp. 81-88
    • Locatelli, M.1    Raber, U.2
  • 36
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and linear programming
    • 916001 0637.90078 10.1007/BF02592948
    • Murty K.G.; Kabadi S.N.: Some NP-complete problems in quadratic and linear programming. Math. Program. 39, 117-129 (1987)
    • (1987) Math. Program. , vol.39 , pp. 117-129
    • Murty, K.G.1    Kabadi, S.N.2
  • 37
    • 0034442088 scopus 로고    scopus 로고
    • Semidefinite programming based test for matrix copositivity
    • Parrilo P.A.: Semidefinite programming based test for matrix copositivity. Proc. 39th IEEE Conf. Decis. Control 5, 4624-4629 (2000)
    • (2000) Proc. 39th IEEE Conf. Decis. Control , vol.5 , pp. 4624-4629
    • Parrilo, P.A.1
  • 38
    • 0031674391 scopus 로고    scopus 로고
    • Copositive relaxation for general quadratic programming
    • 1618092 0904.90126 10.1080/10556789808805692
    • Quist A.J.; de Klerk E.; Roos C.; Terlaky T.: Copositive relaxation for general quadratic programming. Optim. Methods Softw. 9, 185-209 (1998)
    • (1998) Optim. Methods Softw. , vol.9 , pp. 185-209
    • Quist, A.J.1    De Klerk, E.2    Roos, C.3    Terlaky, T.4
  • 39
    • 0023311198 scopus 로고
    • Convex programs with an additional reverse convex constraint
    • 880996 0585.90071 10.1007/BF00938217
    • Tuy H.: Convex programs with an additional reverse convex constraint. J. Optim. Theor. Appl. 52, 463-486 (1987)
    • (1987) J. Optim. Theor. Appl. , vol.52 , pp. 463-486
    • Tuy, H.1
  • 40
    • 0002126665 scopus 로고
    • Criteria for copositive matrices
    • 852891 0598.15017 10.1016/0024-3795(86)90246-6
    • Väliaho H.: Criteria for copositive matrices. Linear Algebra Appl 81, 19-34 (1986)
    • (1986) Linear Algebra Appl , vol.81 , pp. 19-34
    • Väliaho, H.1
  • 41
    • 0042092622 scopus 로고
    • Quadratic-programming criteria for copositive matrices
    • 1005242 0681.15012 10.1016/0024-3795(89)90076-1
    • Väliaho H.: Quadratic-programming criteria for copositive matrices. Linear Algebra Appl. 119, 163-182 (1989)
    • (1989) Linear Algebra Appl. , vol.119 , pp. 163-182
    • Väliaho, H.1
  • 42
    • 55549123838 scopus 로고    scopus 로고
    • Algorithms for determining the copositivity of a given symmetric matrix
    • 2469315 1161.65033 10.1016/j.laa.2008.07.028
    • Yang S.; Li X.: Algorithms for determining the copositivity of a given symmetric matrix. Linear Algebra Appl. 430, 609-618 (2009)
    • (2009) Linear Algebra Appl. , vol.430 , pp. 609-618
    • Yang, S.1    Li, X.2
  • 43
    • 80051720515 scopus 로고    scopus 로고
    • Depth-first simplicial partition for copositivity detection, with an application to Maxclique
    • 2826108 1226.65037 10.1080/10556788.2010.544310
    • Žilinskas J.; Dür M.: Depth-first simplicial partition for copositivity detection, with an application to Maxclique. Optim. Methods. Softw. 26, 499-510 (2011)
    • (2011) Optim. Methods. Softw. , vol.26 , pp. 499-510
    • Žilinskas, J.1    Dür, M.2


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