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Volumn 110, Issue 3, 2007, Pages 521-541

Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions

Author keywords

Binary constraints; Global optimality conditions; Lagrange multipliers; Non convex quadratic minimization; Quadratic inequality constraints

Indexed keywords

NUMERICAL METHODS; OPTIMIZATION; PROBLEM SOLVING;

EID: 34249854587     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0012-5     Document Type: Article
Times cited : (89)

References (24)
  • 1
    • 0034551040 scopus 로고    scopus 로고
    • Global optimality conditions for quadratic optimization problems with binary constraints
    • Beck, A., Teboulle, M.: Global optimality conditions for quadratic optimization problems with binary constraints. SIAM J. Optim. 11, 179-188 (2000)
    • (2000) SIAM J. Optim , vol.11 , pp. 179-188
    • Beck, A.1    Teboulle, M.2
  • 3
    • 0034378311 scopus 로고    scopus 로고
    • A note on digonally dominat matrices
    • Dahl, G.: A note on digonally dominat matrices. Linear Algebra Appl. 317, 217-224 (2000)
    • (2000) Linear Algebra Appl , vol.317 , pp. 217-224
    • Dahl, G.1
  • 4
    • 34249846955 scopus 로고    scopus 로고
    • Derinkuyu, K., Pinar, M.C.: On the S-procedure and some variants, Math. Methods Oper. Res. (see http://www.ie.bilkent.edu.tr/mustafap/pubs/)
    • Derinkuyu, K., Pinar, M.C.: On the S-procedure and some variants, Math. Methods Oper. Res. (see http://www.ie.bilkent.edu.tr/mustafap/pubs/)
  • 5
    • 0008980611 scopus 로고    scopus 로고
    • Dür, M., Horst, R., Locatelli, M.: Necessary and sufficient global optimality conditions for convex maximization revisited. X Math. Anal. Appl. 217(2), 637-649 (1998)
    • Dür, M., Horst, R., Locatelli, M.: Necessary and sufficient global optimality conditions for convex maximization revisited. X Math. Anal. Appl. 217(2), 637-649 (1998)
  • 6
    • 0242420026 scopus 로고    scopus 로고
    • Dual conditions characterizing optimality for convex multi-objective programs
    • Glover, B.M., Jeyakumar, V., Rubinov, A.M.: Dual conditions characterizing optimality for convex multi-objective programs. Math. Progr. 84, 201-217 (1999)
    • (1999) Math. Progr , vol.84 , pp. 201-217
    • Glover, B.M.1    Jeyakumar, V.2    Rubinov, A.M.3
  • 7
    • 0030135235 scopus 로고    scopus 로고
    • Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions
    • Glover, B.M., Ishizuka, Y., Jeyakumar, V., Tuan, H.D.: Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions. SIAM J. Optim. 6, 362-372 (1996)
    • (1996) SIAM J. Optim , vol.6 , pp. 362-372
    • Glover, B.M.1    Ishizuka, Y.2    Jeyakumar, V.3    Tuan, H.D.4
  • 8
    • 0035576919 scopus 로고    scopus 로고
    • Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints
    • Hiriart-Urruty, J.B.: Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints. X Global Optim. 21, 445-455 (2001)
    • (2001) X Global Optim , vol.21 , pp. 445-455
    • Hiriart-Urruty, J.B.1
  • 9
    • 0346144114 scopus 로고    scopus 로고
    • Conditions for global optimality 2
    • Hiriart-Urruty, J.B.: Conditions for global optimality 2. J. Global Optim. 13, 349-367 (1998)
    • (1998) J. Global Optim , vol.13 , pp. 349-367
    • Hiriart-Urruty, J.B.1
  • 13
    • 29144527037 scopus 로고    scopus 로고
    • The strong conical hull intersection property for convex programming
    • Jeyakumar, V. The strong conical hull intersection property for convex programming. Math. Program. Ser A, 106, 81-92 (2006)
    • (2006) Math. Program. Ser A , vol.106 , pp. 81-92
    • Jeyakumar, V.1
  • 14
    • 33748317912 scopus 로고    scopus 로고
    • Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints
    • in press
    • Jeyakumar, V., Rubinov, A.M., Wu, Z. Y.: Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints. J. Global Optim. (in press)
    • J. Global Optim
    • Jeyakumar, V.1    Rubinov, A.M.2    Wu, Z.Y.3
  • 15
    • 0027901827 scopus 로고
    • Generalizations of the trust region problem
    • Moré, J.: Generalizations of the trust region problem. Optim. Meth. Soft. 2, 189-209 (1993)
    • (1993) Optim. Meth. Soft , vol.2 , pp. 189-209
    • Moré, J.1
  • 17
    • 0026115796 scopus 로고
    • Construction of test problems in quadratic bivalent programming
    • Pardalos, P.M.: Construction of test problems in quadratic bivalent programming. ACM Trans. Math. Software 17(1), 74-37 (1991)
    • (1991) ACM Trans. Math. Software , vol.17 , Issue.1 , pp. 74-37
    • Pardalos, P.M.1
  • 18
    • 0031285896 scopus 로고    scopus 로고
    • Optimization conditions for the minimization of a quadratic with two quadratic constraints
    • Peng, J.M., Yuan, Y.: Optimization conditions for the minimization of a quadratic with two quadratic constraints. SIAM J. Optim. 7(3), 579-594 (1997)
    • (1997) SIAM J. Optim , vol.7 , Issue.3 , pp. 579-594
    • Peng, J.M.1    Yuan, Y.2
  • 19
    • 4844219620 scopus 로고    scopus 로고
    • Sufficient global optimality conditions for bivalent quadratic optimization
    • Pinar, M.C.: Sufficient global optimality conditions for bivalent quadratic optimization. J. Optim. Theor. Appl. 122(2), 433-440 (2004)
    • (2004) J. Optim. Theor. Appl , vol.122 , Issue.2 , pp. 433-440
    • Pinar, M.C.1
  • 20
    • 0032259651 scopus 로고    scopus 로고
    • Convexity of quadratic transformations and its use in control and optimization
    • Polyak, B.T.: Convexity of quadratic transformations and its use in control and optimization. J. Optim. Theor. Appl. 99, 553-583 (1998)
    • (1998) J. Optim. Theor. Appl , vol.99 , pp. 553-583
    • Polyak, B.T.1
  • 22
    • 0001219945 scopus 로고
    • Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations
    • Stern, R., Wolkowicz, H.: Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5, 286-313 (1995)
    • (1995) SIAM J. Optim , vol.5 , pp. 286-313
    • Stern, R.1    Wolkowicz, H.2
  • 23
    • 0348036016 scopus 로고    scopus 로고
    • Global optimality conditions for nonconvex optimization
    • Strekalovsky, A.: Global optimality conditions for nonconvex optimization. J. Global Optim. 12(4), 415-434 (1998)
    • (1998) J. Global Optim , vol.12 , Issue.4 , pp. 415-434
    • Strekalovsky, A.1
  • 24
    • 0002182462 scopus 로고
    • The S-procedure in nonlinear control theory
    • Yakubovich, V. A.: The S-procedure in nonlinear control theory. Vestnik Leningr. Univ. 4, 73-93 (1977)
    • (1977) Vestnik Leningr. Univ , vol.4 , pp. 73-93
    • Yakubovich, V.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.