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Volumn 49, Issue 1, 2011, Pages 1-14

Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems

Author keywords

Alternative theorems; Linear equality constraints; Quadratic constraints; Quadratic nonconvex optimization; Regularized Lagrangian; Strong duality; Trust region problems

Indexed keywords

ALTERNATIVE THEOREM; LAGRANGIAN; LINEAR EQUALITY CONSTRAINTS; NONCONVEX OPTIMIZATION; QUADRATIC CONSTRAINT; STRONG DUALITY; TRUST REGION;

EID: 78650749541     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-009-9518-8     Document Type: Article
Times cited : (9)

References (30)
  • 1
    • 70450200104 scopus 로고    scopus 로고
    • Strong duality for the CDT subproblem: A necessary and sufficient sondition
    • 10.1137/07070601X
    • W.B. Ai S.Z. Zhang 2009 Strong duality for the CDT subproblem: a necessary and sufficient sondition SIAM J. Optim. 19 1735 1756 10.1137/07070601X
    • (2009) SIAM J. Optim. , vol.19 , pp. 1735-1756
    • Ai, W.B.1    Zhang, S.Z.2
  • 2
    • 33847613047 scopus 로고    scopus 로고
    • Strong duality in nonconvex quadratic optimization with two quadratic constraints
    • DOI 10.1137/050644471
    • A. Beck Y.C. Eldar 2006 Strong duality in nonconvex quadratic optimization with two quadratic constraints SIAM J. Optim. 17 844 860 10.1137/050644471 (Pubitemid 47265175)
    • (2006) SIAM Journal on Optimization , vol.17 , Issue.3 , pp. 844-860
    • Beck, A.1    Eldar, Y.C.2
  • 5
    • 0002336672 scopus 로고
    • A trust region strategy for nonlinear equality constrained optimization
    • P.T. Boggs R.H. Byrd R.B. Schnabel (eds). SIAM Philadelphia
    • Celis M.R., Dennis J.E., Tapia R.A.: A trust region strategy for nonlinear equality constrained optimization. In: Boggs, P.T., Byrd, R.H., Schnabel, R.B. (eds) Numerical Optimization, pp. 71-82. SIAM, Philadelphia (1985)
    • (1985) Numerical Optimization , pp. 71-82
    • Celis, M.R.1    Dennis, J.E.2    Tapia, R.A.3
  • 6
    • 0001499369 scopus 로고
    • Definiteness and semidefiniteness of quadratic forms revisited
    • 10.1016/0024-3795(84)90150-2
    • Y. Chabrillac J.-P. Crouzeix 1984 Definiteness and semidefiniteness of quadratic forms revisited Linear Algebra Appl. 63 283 294 10.1016/0024-3795(84) 90150-2
    • (1984) Linear Algebra Appl. , vol.63 , pp. 283-294
    • Chabrillac, Y.1    Crouzeix, J.-P.2
  • 7
    • 0039012115 scopus 로고    scopus 로고
    • On local solutions of the Celis-Dennis-Tapia subproblem
    • 10.1137/S1052623498335018
    • X.D. Chen Y.X. Yuan 2000 On local solutions of the Celis-Dennis-Tapia subproblem SIAM J. Optim. 10 359 383 10.1137/S1052623498335018
    • (2000) SIAM J. Optim. , vol.10 , pp. 359-383
    • Chen, X.D.1    Yuan, Y.X.2
  • 8
    • 0036471766 scopus 로고    scopus 로고
    • A new trust-region algorithm for equality constrained optimization
    • DOI 10.1023/A:1013764800871
    • T.F. Coleman J. Liu W. Yuan 2002 A new trust-region algorithm for equality constrained optimization Comp. Optim. Appl. 21 2 177 199 10.1023/A:1013764800871 (Pubitemid 34168105)
    • (2002) Computational Optimization and Applications , vol.21 , Issue.2 , pp. 177-199
    • Coleman, T.F.1    Liu, J.2    Yuan, W.3
  • 9
    • 0037958862 scopus 로고
    • On the mapping of quadratic forms
    • 10.1090/S0002-9904-1941-07494-X
    • L.L. Dines 1941 On the mapping of quadratic forms Bull. Am. Math. Soc. 47 494 498 10.1090/S0002-9904-1941-07494-X
    • (1941) Bull. Am. Math. Soc. , vol.47 , pp. 494-498
    • Dines, L.L.1
  • 10
    • 33947705085 scopus 로고    scopus 로고
    • Partial Lagrangian relaxation for general quadratic programming
    • 10.1007/s10288-006-0011-7
    • A. Faye F. Roupin 2007 Partial Lagrangian relaxation for general quadratic programming 4OR Q. J. Oper. Res. 5 75 88 10.1007/s10288-006-0011-7
    • (2007) 4OR Q. J. Oper. Res. , vol.5 , pp. 75-88
    • Faye, A.1    Roupin, F.2
  • 11
    • 1542346048 scopus 로고    scopus 로고
    • The trust region subproblem and semidefinite programming
    • 10.1080/10556780410001647186
    • C. Fortin H. Wolkowicz 2004 The trust region subproblem and semidefinite programming Optim. Methods Softw. 19 41 67 10.1080/10556780410001647186
    • (2004) Optim. Methods Softw. , vol.19 , pp. 41-67
    • Fortin, C.1    Wolkowicz, H.2
  • 13
    • 38049050343 scopus 로고    scopus 로고
    • Constraint qualifications characterizing Lagrangian duality in convex optimization
    • 10.1007/s10957-007-9294-x
    • V. Jeyakumar 2008 Constraint qualifications characterizing Lagrangian duality in convex optimization J. Optim. Theory Appl. 136 31 41 10.1007/s10957-007-9294-x
    • (2008) J. Optim. Theory Appl. , vol.136 , pp. 31-41
    • Jeyakumar, V.1
  • 14
    • 70450277572 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for S-lemma and nonconvex optimization
    • 10.1007/s11081-008-9076-9
    • V. Jeyakumar N.Q. Huy G. Li 2009 Necessary and sufficient conditions for S-lemma and nonconvex optimization Optim. Eng. 10 4 491 503 10.1007/s11081-008- 9076-9
    • (2009) Optim. Eng. , vol.10 , Issue.4 , pp. 491-503
    • Jeyakumar, V.1    Huy, N.Q.2    Li, G.3
  • 15
    • 70450203529 scopus 로고    scopus 로고
    • Alternative theorems for quadratic inequality systems and global quadratic optimization
    • 10.1137/080736090
    • V. Jeyakumar G.M. Lee G. Li 2009 Alternative theorems for quadratic inequality systems and global quadratic optimization SIAM J. Optim. 20 2 983 1001 10.1137/080736090
    • (2009) SIAM J. Optim. , vol.20 , Issue.2 , pp. 983-1001
    • Jeyakumar, V.1    Lee, G.M.2    Li, G.3
  • 16
    • 76549132586 scopus 로고    scopus 로고
    • Nonsmooth vector functions and continuous optimization
    • P.M. Pardalos (eds). Springer New York
    • Jeyakumar V., Luc D.T.: Nonsmooth vector functions and continuous optimization. In: Pardalos, P.M. (eds) Springer Optimization and Its Applications, vol. 10, Springer, New York (2008)
    • (2008) Springer Optimization and Its Applications, Vol. 10
    • Jeyakumar, V.1    Luc, D.T.2
  • 17
    • 34249854587 scopus 로고    scopus 로고
    • Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions
    • DOI 10.1007/s10107-006-0012-5
    • V. Jeyakumar A.M. Rubinov Z.Y. Wu 2007 Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions Math. Program. Ser. A 110 521 541 10.1007/s10107-006-0012-5 (Pubitemid 46862319)
    • (2007) Mathematical Programming , vol.110 , Issue.3 , pp. 521-541
    • Jeyakumar, V.1    Rubinov, A.M.2    Wu, Z.Y.3
  • 18
    • 34447294293 scopus 로고    scopus 로고
    • Kuhn-Tucker sufficiency for global minimum of multi-extremal mathematical programming problems
    • 10.1016/j.jmaa.2007.02.013
    • V. Jeyakumar S. Srisatkunarajah N.Q. Huy 2007 Kuhn-Tucker sufficiency for global minimum of multi-extremal mathematical programming problems J. Math. Anal. Appl. 335 779 788 10.1016/j.jmaa.2007.02.013
    • (2007) J. Math. Anal. Appl. , vol.335 , pp. 779-788
    • Jeyakumar, V.1    Srisatkunarajah, S.2    Huy, N.Q.3
  • 19
    • 33947667140 scopus 로고    scopus 로고
    • SDP relaxations in combinatorial optimization from a Lagrangian viewpoint, in advances in convex analysis and global optimization (Pythagorion, 2000)
    • Kluwer, Dordrecht
    • Lemarechal, C., Oustry, F.: SDP relaxations in combinatorial optimization from a Lagrangian viewpoint, in advances in convex analysis and global optimization (Pythagorion, 2000). Nonconvex Optim. Appl., vol. 54, pp. 119-134. Kluwer, Dordrecht (2001)
    • (2001) Nonconvex Optim. Appl. , vol.54 , pp. 119-134
    • Lemarechal, C.1    Oustry, F.2
  • 20
    • 0001220590 scopus 로고    scopus 로고
    • Semidefinite programming relaxations of nonconvex quadratic optimization
    • H. Wolkowicz R. Saigal L. Vandenberghe (eds). Kluwer Boston
    • Nesterov Y., Wolkowicz H., Ye Y.Y.: Semidefinite programming relaxations of nonconvex quadratic optimization. In: Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds) Handbook of Semidefinite Programming, pp. 361-419. Kluwer, Boston (2000)
    • (2000) Handbook of Semidefinite Programming , pp. 361-419
    • Nesterov, Y.1    Wolkowicz, H.2    Ye, Y.Y.3
  • 22
    • 3042732867 scopus 로고    scopus 로고
    • A new linearization technique for multi-quadratic 0-1 programming problems
    • 10.1016/j.orl.2004.03.005
    • P.M. Pardalos O. Prokopyev W. Chaovalitwongse 2004 A new linearization technique for multi-quadratic 0-1 programming problems Oper. Res. Lett. 32 6 517 522 10.1016/j.orl.2004.03.005
    • (2004) Oper. Res. Lett. , vol.32 , Issue.6 , pp. 517-522
    • Pardalos, P.M.1    Prokopyev, O.2    Chaovalitwongse, W.3
  • 24
    • 0031285896 scopus 로고    scopus 로고
    • Optimality conditions for the minimization of a quadratic with two quadratic constraints
    • 10.1137/S1052623494261520
    • J.M. Peng Y.X. Yuan 1997 Optimality conditions for the minimization of a quadratic with two quadratic constraints SIAM J. Optim. 7 579 594 10.1137/S1052623494261520
    • (1997) SIAM J. Optim. , vol.7 , pp. 579-594
    • Peng, J.M.1    Yuan, Y.X.2
  • 25
    • 34548491396 scopus 로고    scopus 로고
    • A survey of the S-lemma
    • DOI 10.1137/S003614450444614X
    • I. Polik T. Terlaky 2007 A survey of S-lemma SIAM Rev. 49 371 418 10.1137/S003614450444614X (Pubitemid 47377690)
    • (2007) SIAM Review , vol.49 , Issue.3 , pp. 371-418
    • Polik, I.1    Terlaky, T.2
  • 26
    • 34249955300 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • 10.1007/BF01588787
    • M.J.D. Powell Y. Yuan 1991 A trust region algorithm for equality constrained optimization Math. Program. 49 189 211 10.1007/BF01588787
    • (1991) Math. Program. , vol.49 , pp. 189-211
    • Powell, M.J.D.1    Yuan, Y.2
  • 27
    • 0001219945 scopus 로고
    • Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations
    • 10.1137/0805016
    • R.J. Stern H. Wolkowicz 1995 Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations SIAM J. Optim. 5 286 313 10.1137/0805016
    • (1995) SIAM J. Optim. , vol.5 , pp. 286-313
    • Stern, R.J.1    Wolkowicz, H.2
  • 28
    • 0035729439 scopus 로고    scopus 로고
    • A Conic Trust-Region Method for Nonlinearly Constrained Optimization
    • DOI 10.1023/A:1012955122229
    • W.Y. Sun Y.X. Yuan 2001 A conic trust-region method for nonlinearly constrained optimization Ann. Oper. Res. 103 175 191 10.1023/A:1012955122229 (Pubitemid 33634407)
    • (2001) Annals of Operations Research , vol.103 , Issue.1-4 , pp. 175-191
    • Sun, W.1    Yuan, Y.-X.2
  • 29
    • 1542380911 scopus 로고    scopus 로고
    • New results of quadratic minimization
    • 10.1137/S105262340139001X
    • Y. Ye S.Z. Zhang 2003 New results of quadratic minimization SIAM J. Optim. 14 245 267 10.1137/S105262340139001X
    • (2003) SIAM J. Optim. , vol.14 , pp. 245-267
    • Ye, Y.1    Zhang, S.Z.2
  • 30
    • 0002765829 scopus 로고
    • On a subproblem of trust region algorithms for constrained optimization
    • 10.1007/BF01580852
    • Y.X. Yuan 1990 On a subproblem of trust region algorithms for constrained optimization Math. Program. 47 53 63 10.1007/BF01580852
    • (1990) Math. Program. , vol.47 , pp. 53-63
    • Yuan, Y.X.1


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