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Volumn 56, Issue 3, 2013, Pages 1045-1072

Generalized S-Lemma and strong duality in nonconvex quadratic programming

Author keywords

Generalized S Lemma; Global optimization; Nonconvex quadratic optimization; Strong duality; Topological minimax theorem

Indexed keywords

CONSTRAINED QUADRATIC OPTIMIZATION; GENERALIZED S-LEMMA; MINIMAX THEOREM; NON CONVEX QUADRATIC PROGRAMMING; NONCONVEX QUADRATIC OPTIMIZATION; QUADRATIC PROGRAMS; SEMIDEFINITE PROGRAMS; STRONG DUALITY;

EID: 84879696077     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-012-9917-0     Document Type: Conference Paper
Times cited : (26)

References (35)
  • 1
    • 33847613047 scopus 로고    scopus 로고
    • Strong duality in nonconvex quadratic optimization with two quadratic constraints
    • 10.1137/050644471
    • Beck A.; Eldar Y.C.: Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J. Optim. 17, 844-860 (2006)
    • (2006) SIAM J. Optim. , vol.17 , pp. 844-860
    • Beck, A.1    Eldar, Y.C.2
  • 5
    • 0037958862 scopus 로고
    • On the mapping of quadratic forms
    • 10.1090/S0002-9904-1941-07494-X
    • Dines L.: On the mapping of quadratic forms. Bull. Am. Math. Soc. 47, 494-498 (1941)
    • (1941) Bull. Am. Math. Soc. , vol.47 , pp. 494-498
    • Dines, L.1
  • 7
    • 0001641947 scopus 로고
    • Uber das vorkommen definiter und semidefiniter formen in scharen quadratischer formen
    • 10.1007/BF01258188
    • Finsler P.: Uber das vorkommen definiter und semidefiniter formen in scharen quadratischer formen. Comment. Math. Helv. 9, 188-192 (1936-1937)
    • (1936) Comment. Math. Helv. , vol.9 , pp. 188-192
    • Finsler, P.1
  • 8
    • 0007469744 scopus 로고
    • A collection of test problems for constrained global optimization algorithms
    • Springer
    • Floudas, C.; Pardalos, P.: A collection of test problems for constrained global optimization algorithms. Lecture Notes in Comput. Sci, vol. 455, Springer (1990)
    • (1990) Lecture Notes in Comput. Sci , vol.455
    • Floudas, C.1    Pardalos, P.2
  • 9
    • 0000201892 scopus 로고    scopus 로고
    • Semidefinite programming relaxation for nonconvex quadratic programs
    • 10.1023/A:1008282830093
    • Fujie T.; Kojima M.: Semidefinite programming relaxation for nonconvex quadratic programs. J. Glob. Opt. 10, 367-380 (1997)
    • (1997) J. Glob. Opt. , vol.10 , pp. 367-380
    • Fujie, T.1    Kojima, M.2
  • 11
    • 0141938582 scopus 로고    scopus 로고
    • Permanently going back and forth between the 'quadratic world' and the 'convexity world' in optimization
    • 10.1007/s00245-001-0034-6
    • Hiriart-Urruty J.-B.; Torki M.: Permanently going back and forth between the 'quadratic world' and the 'convexity world' in optimization. Appl. Math. Optim. 45, 169-184 (2002)
    • (2002) Appl. Math. Optim. , vol.45 , pp. 169-184
    • Hiriart-Urruty, J.-B.1    Torki, M.2
  • 12
    • 58249127199 scopus 로고    scopus 로고
    • A lyapunov variable-free KYP lemma for SISO continuous systems
    • 10.1109/TAC.2008.2007156
    • Hoang H.G.; Tuan H.D.; Apkarian P.: A lyapunov variable-free KYP lemma for SISO continuous systems. IEEE Trans. Autom. Control. 53, 2669-2673 (2008)
    • (2008) IEEE Trans. Autom. Control. , vol.53 , pp. 2669-2673
    • Hoang, H.G.1    Tuan, H.D.2    Apkarian, P.3
  • 13
    • 70450203529 scopus 로고    scopus 로고
    • Alternative theorems for quadratic inequality systems and global quadratic optimization
    • 10.1137/080736090
    • Jeyakumar V.; Lee G.M.; Li G.Y.: Alternative theorems for quadratic inequality systems and global quadratic optimization. SIAM J. Optim. 20, 983-1001 (2009)
    • (2009) SIAM J. Optim. , vol.20 , pp. 983-1001
    • Jeyakumar, V.1    Lee, G.M.2    Li, G.Y.3
  • 14
    • 78650749541 scopus 로고    scopus 로고
    • Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems
    • 10.1007/s10898-009-9518-8
    • Jeyakumar V.; Li G.: Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems. J. Glob. Optim. 49, 1-14 (2011)
    • (2011) J. Glob. Optim. , vol.49 , pp. 1-14
    • Jeyakumar, V.1    Li, G.2
  • 15
    • 0242302674 scopus 로고    scopus 로고
    • Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations
    • 10.1023/A:1025794313696
    • Kim S.; Kojima M.: Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Comput. Optim. Appl. 26, 143-154 (2003)
    • (2003) Comput. Optim. Appl. , vol.26 , pp. 143-154
    • Kim, S.1    Kojima, M.2
  • 16
    • 0036883726 scopus 로고    scopus 로고
    • On the finite convergence of successive SDP relaxation methods
    • 10.1016/S0377-2217(02)00298-9
    • Kojima M.; Tunçel L.: On the finite convergence of successive SDP relaxation methods. Eur. J. Oper. Res. 143, 325-341 (2002)
    • (2002) Eur. J. Oper. Res. , vol.143 , pp. 325-341
    • Kojima, M.1    Tunçel, L.2
  • 17
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • 10.1137/S1052623400366802
    • Lasserre J.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11, 796-817 (2001)
    • (2001) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.1
  • 18
    • 34548491396 scopus 로고    scopus 로고
    • A survey of the S-Lemma
    • 10.1137/S003614450444614X
    • Polik I.; Terlaky T.: A survey of the S-Lemma. SIAM Rev. 49, 371-418 (2007)
    • (2007) SIAM Rev. , vol.49 , pp. 371-418
    • Polik, I.1    Terlaky, T.2
  • 19
    • 0032259651 scopus 로고    scopus 로고
    • Convexity of quadratic transformations and its use in control and optimization
    • 10.1023/A:1021798932766
    • Polyak B.T.: Convexity of quadratic transformations and its use in control and optimization. J. Optim. Theory Appl. 99, 353-383 (1998)
    • (1998) J. Optim. Theory Appl. , vol.99 , pp. 353-383
    • Polyak, B.T.1
  • 20
    • 3543116866 scopus 로고    scopus 로고
    • A further improvement of a minimax theorem of Borhenshtein and Shul'man
    • Ricceri B.: A further improvement of a minimax theorem of Borhenshtein and Shul'man. J. Nonlinear Convex Anal. 2, 279-283 (2001)
    • (2001) J. Nonlinear Convex Anal. , vol.2 , pp. 279-283
    • Ricceri, B.1
  • 21
    • 0001223006 scopus 로고
    • Computationally related problems
    • 10.1137/0203021
    • Sahni S.: Computationally related problems. SIAM J. Comput. 3, 263-279 (1974)
    • (1974) SIAM J. Comput. , vol.3 , pp. 263-279
    • Sahni, S.1
  • 24
    • 0002909079 scopus 로고
    • Dual estimates in multiextremal problems
    • 10.1007/BF00122430
    • Shor N.Z.: Dual estimates in multiextremal problems. J. Glob. Optim. 2, 411-418 (1992)
    • (1992) J. Glob. Optim. , vol.2 , pp. 411-418
    • Shor, N.Z.1
  • 25
    • 0038386380 scopus 로고    scopus 로고
    • On cones of nonnegative quadratic functions
    • 10.1287/moor.28.2.246.14485
    • Sturm J.F.; Zhang S.: On cones of nonnegative quadratic functions. Math. Oper. Res. 28, 246-267 (2003)
    • (2003) Math. Oper. Res. , vol.28 , pp. 246-267
    • Sturm, J.F.1    Zhang, S.2
  • 27
    • 80051668529 scopus 로고    scopus 로고
    • A new minimax theorem with applications
    • 10.1007/s10898-010-9591-z
    • Tuy H.: A new minimax theorem with applications. J. Glob. Optim. 50, 371-378 (2011)
    • (2011) J. Glob. Optim. , vol.50 , pp. 371-378
    • Tuy, H.1
  • 28
    • 0034353741 scopus 로고    scopus 로고
    • Monotonic optimization: Problems and solution approaches
    • 10.1137/S1052623499359828
    • Tuy H.: Monotonic optimization: problems and solution approaches. SIAM J. Optim. 11, 464-494 (2000)
    • (2000) SIAM J. Optim. , vol.11 , pp. 464-494
    • Tuy, H.1
  • 29
    • 67349216977 scopus 로고    scopus 로고
    • Global optimization of polynomials using the truncated tagency variety and sums of squares
    • 10.1137/080719212
    • Vui H.H.; Son P.T.: Global optimization of polynomials using the truncated tagency variety and sums of squares. SIAM J. Optim. 19, 941-951 (2008)
    • (2008) SIAM J. Optim. , vol.19 , pp. 941-951
    • Vui, H.H.1    Son, P.T.2
  • 30
    • 67349186860 scopus 로고    scopus 로고
    • Solving polynomial optimization problems via the truncated tangency variety and sums of squares
    • 10.1016/j.jpaa.2009.03.014
    • Vui H.H.; Son P.T.: Solving polynomial optimization problems via the truncated tangency variety and sums of squares. J. Pure Appl. Algebra. 213, 2167-2176 (2009)
    • (2009) J. Pure Appl. Algebra. , vol.213 , pp. 2167-2176
    • Vui, H.H.1    Son, P.T.2
  • 31
    • 0002182462 scopus 로고
    • The S-procedure in nonlinear control theory
    • (English translation)
    • Yakubovich V.A.: The S-procedure in nonlinear control theory. Vestnik Leningr. Univ. Math. 4, 73-93 (1977) (English translation)
    • (1977) Vestnik Leningr. Univ. Math. , vol.4 , pp. 73-93
    • Yakubovich, V.A.1
  • 32
    • 1542380911 scopus 로고    scopus 로고
    • New results on quadratic optimization
    • 10.1137/S105262340139001X
    • Ye Y.; Zhang S.: New results on quadratic optimization. SIAM J. Optim. 14, 245-267 (2003)
    • (2003) SIAM J. Optim. , vol.14 , pp. 245-267
    • Ye, Y.1    Zhang, S.2
  • 33
    • 0002765829 scopus 로고
    • On a subproblem of trust region algorithms for constrained optimization
    • 10.1007/BF01580852
    • Yuan Y.: On a subproblem of trust region algorithms for constrained optimization. Math. Program. 47, 53-83 (1990)
    • (1990) Math. Program. , vol.47 , pp. 53-83
    • Yuan, Y.1
  • 34
    • 77958519712 scopus 로고    scopus 로고
    • Some equivalent results with Yakubovich's S-Lemma
    • 10.1137/080744219
    • Zi-Zong Y.; Jin-Hai G.: Some equivalent results with Yakubovich's S-Lemma. SIAM J. Control Optim. 48, 4474-4480 (2010)
    • (2010) SIAM J. Control Optim. , vol.48 , pp. 4474-4480
    • Zi-Zong, Y.1    Jin-Hai, G.2
  • 35
    • 84858861152 scopus 로고    scopus 로고
    • On zero duality in nonconvex quadratic programming problems
    • doi: 10.1007/s10898-011-9660-y
    • Zheng, X.J.; Sun, X.L.; Li, D.; Xu, Y.F.: On zero duality in nonconvex quadratic programming problems. J. Glob. Optim. doi: 10.1007/s10898-011-9660-y
    • J. Glob. Optim.
    • Zheng, X.J.1    Sun, X.L.2    Li, D.3    Xu, Y.F.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.