메뉴 건너뛰기




Volumn 47, Issue 1, 2010, Pages 33-59

Extended duality for nonlinear programming

Author keywords

Duality gap; Extended duality; Global optimization; Nonlinear programming

Indexed keywords

BRANCH AND BOUNDS; DUAL FUNCTION; DUAL METHOD; DUALITY GAP; DUALITY THEORY; EXACT PENALTIES; EXTENDED DUALITY; FEASIBLE SET; FUNCTION VALUES; FUNDAMENTAL LIMITS; ILL-CONDITIONING; LAGRANGIAN THEORY; LOWER BOUNDS; MIXED-INTEGER; NETWORK OPTIMIZATION; NON-LINEAR OPTIMIZATION; NONCONVEX; NONCONVEX PROBLEM; NONLINEAR LAGRANGIAN; OPTIMIZATION ALGORITHMS; SEARCH TECHNIQUE; SOLUTION QUALITY; THEORETICAL FOUNDATIONS;

EID: 77956766681     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9208-3     Document Type: Article
Times cited : (17)

References (26)
  • 1
    • 0016990134 scopus 로고
    • Estimates of the duality gap in nonconvex optimization
    • 0366.90102 10.1287/moor.1.3.225 449695
    • J.P. Aubin I. Ekeland 1976 Estimates of the duality gap in nonconvex optimization Math. Oper. Res. 1 225 245 0366.90102 10.1287/moor.1.3.225 449695
    • (1976) Math. Oper. Res. , vol.1 , pp. 225-245
    • Aubin, J.P.1    Ekeland, I.2
  • 2
    • 0028257449 scopus 로고
    • Global optimization by reducing the duality gap
    • 10.1007/BF01582066 1268607
    • A. Ben-Tal G. Eiger V. Gershovitz 1994 Global optimization by reducing the duality gap Math. Program. 63 193 212 10.1007/BF01582066 1268607
    • (1994) Math. Program. , vol.63 , pp. 193-212
    • Ben-Tal, A.1    Eiger, G.2    Gershovitz, V.3
  • 3
    • 0020138998 scopus 로고
    • Distributed dynamic programming
    • 10.1109/TAC.1982.1102980 680319
    • D.P. Bertsekas 1982 Distributed dynamic programming Trans. Autom. Control AC-27 3 610 616 10.1109/TAC.1982.1102980 680319
    • (1982) Trans. Autom. Control , vol.27 , Issue.3 , pp. 610-616
    • Bertsekas, D.P.1
  • 5
    • 34848874471 scopus 로고    scopus 로고
    • On the absence of duality gap for Lagrange-type functions
    • 1135.90428 2127801
    • R.S. Burachik A. Rubinov 2005 On the absence of duality gap for Lagrange-type functions J. Indust. Manag. Optim. 1 1 33 38 1135.90428 2127801
    • (2005) J. Indust. Manag. Optim. , vol.1 , Issue.1 , pp. 33-38
    • Burachik, R.S.1    Rubinov, A.2
  • 6
    • 0026118632 scopus 로고
    • Calmness and exact penalization
    • 0734.90090 10.1137/0329027 1092740
    • J.V. Burke 1991 Calmness and exact penalization SIAM J. Control Optim. 29 493 497 0734.90090 10.1137/0329027 1092740
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 493-497
    • Burke, J.V.1
  • 7
    • 0026190240 scopus 로고
    • An exact penalization viewpoint of constrained optimization
    • 0737.90060 10.1137/0329054 1111671
    • J.V. Burke 1991 An exact penalization viewpoint of constrained optimization SIAM J. Control Optim. 29 968 998 0737.90060 10.1137/0329054 1111671
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 968-998
    • Burke, J.V.1
  • 10
    • 0036433588 scopus 로고    scopus 로고
    • SNOPT: An SQP algorithm for large-scale constrained optimization
    • 1027.90111 10.1137/S1052623499350013 1922505
    • P.E. Gill W. Murray M. Saunders 2002 SNOPT: An SQP algorithm for large-scale constrained optimization SIAM J. Optim. 12 979 1006 1027.90111 10.1137/S1052623499350013 1922505
    • (2002) SIAM J. Optim. , vol.12 , pp. 979-1006
    • Gill, P.E.1    Murray, W.2    Saunders, M.3
  • 11
    • 19844376473 scopus 로고    scopus 로고
    • 1-penalty method for nonlinear optimization
    • Rutherford Appleton Laboratory Chilton, Oxfordshire, UK, November
    • 1-penalty method for nonlinear optimization. Technical Report RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK, November (2003)
    • (2003) Technical Report RAL-TR-2003-022
    • Gould, N.I.M.1    Orban, D.2    Toint, P.L.3
  • 12
    • 0141740372 scopus 로고    scopus 로고
    • A unified augmented Lagrangian approach to duality and exact penalization
    • 1082.90135 10.1287/moor.28.3.533.16395 1997249
    • X.X. Huang X.Q. Yang 2003 A unified augmented Lagrangian approach to duality and exact penalization Math. Oper. Res. 28 3 533 552 1082.90135 10.1287/moor.28.3.533.16395 1997249
    • (2003) Math. Oper. Res. , vol.28 , Issue.3 , pp. 533-552
    • Huang, X.X.1    Yang, X.Q.2
  • 13
    • 0033094194 scopus 로고    scopus 로고
    • Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization
    • 10.1162/evco.1999.7.1.19
    • S. Koziel Z. Michalewics 1999 Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization Evolut. Comput. 7 1 19 44 10.1162/evco.1999.7.1.19
    • (1999) Evolut. Comput. , vol.7 , Issue.1 , pp. 19-44
    • Koziel, S.1    Michalewics, Z.2
  • 14
    • 0012228831 scopus 로고    scopus 로고
    • Error bounds in mathematical programming
    • Luo, Z.Q., Pang, J.S.: Error bounds in mathematical programming. Math. Program. Ser. B, 88(2) (2000)
    • (2000) Math. Program. Ser. B , vol.88 , Issue.2
    • Luo, Z.Q.1    Pang, J.S.2
  • 15
    • 39749098591 scopus 로고    scopus 로고
    • A geometric framework for nonconvex optimization duality using augmented lagrangian functions
    • DOI 10.1007/s10898-006-9122-0, Advances in Complementarity, Duality, and Global Optimization
    • A. Nedić A. Ozdaglar 2008 A geometric framework for nonconvex optimization duality using augmented Lagrangian functions J. Glob. Optim. 40 4 545 573 10.1007/s10898-006-9122-0 (Pubitemid 351304416)
    • (2008) Journal of Global Optimization , vol.40 , Issue.4 , pp. 545-573
    • Nedich, A.1    Ozdaglar, A.2
  • 16
    • 0000150038 scopus 로고    scopus 로고
    • Error bounds in mathematical programming
    • J.S. Pang 1997 Error bounds in mathematical programming Math. Program. 79 299 332
    • (1997) Math. Program. , vol.79 , pp. 299-332
    • Pang, J.S.1
  • 17
    • 0016059769 scopus 로고
    • Augmented Lagrangian multiplier functions and duality in nonconvex programming
    • 0257.90046 10.1137/0312021 384163
    • R.T. Rockafellar 1974 Augmented Lagrangian multiplier functions and duality in nonconvex programming SIAM J. Control Optim. 12 268 285 0257.90046 10.1137/0312021 384163
    • (1974) SIAM J. Control Optim. , vol.12 , pp. 268-285
    • Rockafellar, R.T.1
  • 19
    • 0033261453 scopus 로고    scopus 로고
    • Decreasing functions with applications to penalization
    • 0955.90127 10.1137/S1052623497326095 1742317
    • A.M. Rubinov B.M. Glover X.Q. Yang 1999 Decreasing functions with applications to penalization SIAM J. Optim. 10 289 313 0955.90127 10.1137/S1052623497326095 1742317
    • (1999) SIAM J. Optim. , vol.10 , pp. 289-313
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 20
    • 0000606438 scopus 로고    scopus 로고
    • Modified Lagrangian and penalty functions in continuous optimization
    • 1030.90120 10.1080/02331939908844460 1776176
    • A.M. Rubinov B.M. Glover X.Q. Yang 1999 Modified Lagrangian and penalty functions in continuous optimization Optimization 46 327 351 1030.90120 10.1080/02331939908844460 1776176
    • (1999) Optimization , vol.46 , pp. 327-351
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 21
    • 25444518752 scopus 로고    scopus 로고
    • On solving nonconvex optimization problems by reducing the duality gap
    • DOI 10.1007/s10898-004-1947-9
    • H. Tuy 2005 On solving nonconvex optimization problems by reducing the duality gap J. Glob. Optim. 32 349 365 1149.90388 10.1007/s10898-004-1947-9 2177623 (Pubitemid 41367537)
    • (2005) Journal of Global Optimization , vol.32 , Issue.3 , pp. 349-365
    • Tuy, H.1
  • 22
    • 43949152886 scopus 로고
    • Global optimization of statistical functions with simulated annealing
    • 0789.62095
    • G.D. Ferrier W.L. Goffe J. Rogers 1994 Global optimization of statistical functions with simulated annealing J. Econ. 60 1 65 99 0789.62095
    • (1994) J. Econ. , vol.60 , Issue.1 , pp. 65-99
    • Ferrier, G.D.1    Goffe, W.L.2    Rogers, J.3
  • 26
    • 0035621414 scopus 로고    scopus 로고
    • A nonlinear Lagrangian approach to constraint optimization problems
    • 0999.90049 10.1137/S1052623400371806 1855224
    • X.Q. Yang X.X. Huang 2001 A nonlinear Lagrangian approach to constraint optimization problems SIAM J. Optim. 11 1119 1144 0999.90049 10.1137/S1052623400371806 1855224
    • (2001) SIAM J. Optim. , vol.11 , pp. 1119-1144
    • Yang, X.Q.1    Huang, X.X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.