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Volumn 9, Issue 1-2, 2001, Pages 169-186

Second-Order Optimality Conditions in Generalized Semi-Infinite Programming

Author keywords

Generalized semi infinite programming; Necessary and sufficient second order optimality conditions; Optimal value function; Second order (parabolically) directionally differentiable; Second order growth condition

Indexed keywords


EID: 0035600085     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011239607220     Document Type: Article
Times cited : (38)

References (27)
  • 1
    • 0001664441 scopus 로고
    • Second-order and related extremality conditions in nonlinear programming
    • Ben-Tal, A.: Second-order and related extremality conditions in nonlinear programming, J. Optim. Theory Appl. 31 (1980), 143-165.
    • (1980) J. Optim. Theory Appl. , vol.31 , pp. 143-165
    • Ben-Tal, A.1
  • 2
    • 0033434223 scopus 로고    scopus 로고
    • Second order optimality conditions based on parabolic second order tangent sets
    • Bonnans, J. F., Cominetti, R. and Shapiro, A.: Second order optimality conditions based on parabolic second order tangent sets, SIAM J. Optim. 9 (1999), 466-492.
    • (1999) SIAM J. Optim. , vol.9 , pp. 466-492
    • Bonnans, J.F.1    Cominetti, R.2    Shapiro, A.3
  • 3
    • 0032096712 scopus 로고    scopus 로고
    • Optimization problems with perturbations, a guided tour
    • Bonnans, J. F. and Shapiro, A.: Optimization problems with perturbations, a guided tour, SIAM Rev. 40 (1998), 228-264.
    • (1998) SIAM Rev. , vol.40 , pp. 228-264
    • Bonnans, J.F.1    Shapiro, A.2
  • 5
    • 0020166920 scopus 로고
    • Differential properties of the marginal function in mathematical programming
    • Gauvin, J. and Dubeau, F.: Differential properties of the marginal function in mathematical programming, Math. Programming Study 19 (1982), 101-119.
    • (1982) Math. Programming Study , vol.19 , pp. 101-119
    • Gauvin, J.1    Dubeau, F.2
  • 7
    • 0023961719 scopus 로고
    • The acceleration radius: A global performance measure for robotic manipulators
    • Graettinger, T. J. and Krogh, B. H.: The acceleration radius: a global performance measure for robotic manipulators, IEEE J. Robotics Automation 4 (1988), 60-69.
    • (1988) IEEE J. Robotics Automation , vol.4 , pp. 60-69
    • Graettinger, T.J.1    Krogh, B.H.2
  • 8
    • 0027657329 scopus 로고
    • Semi-infinite programming: Theory, methods and applications
    • Hettich, R. and Kortanek, K. O.: Semi-infinite programming: theory, methods and applications, SIAM Rev. 35(3) (1993), 380-429.
    • (1993) SIAM Rev. , vol.35 , Issue.3 , pp. 380-429
    • Hettich, R.1    Kortanek, K.O.2
  • 9
    • 0009276017 scopus 로고
    • Semi-infinite programming models in robotics
    • J. Guddat et al. (eds), Parametric Optimization and Related Topics II, Akademie-Verlag, Berlin
    • Hettich, R. and Still, G.: Semi-infinite programming models in robotics, In: J. Guddat et al. (eds), Parametric Optimization and Related Topics II, Math. Res. 62, Akademie-Verlag, Berlin, 1991, pp. 112-118.
    • (1991) Math. Res. , vol.62 , pp. 112-118
    • Hettich, R.1    Still, G.2
  • 10
    • 0001004265 scopus 로고
    • Second order optimality conditions for generalized semi-infinite programming problems
    • Hettich, R. and Still, G.: Second order optimality conditions for generalized semi-infinite programming problems, Optimization 34 (1995), 195-211.
    • (1995) Optimization , vol.34 , pp. 195-211
    • Hettich, R.1    Still, G.2
  • 11
    • 0040055948 scopus 로고    scopus 로고
    • Disjunctive optimization: Critical point theory
    • Jongen, H. Th., Rückmann, J.-J. and Stein, O.: Disjunctive optimization: critical point theory, J. Optim. Theory Appl. 93(2) (1997), 321-336.
    • (1997) J. Optim. Theory Appl. , vol.93 , Issue.2 , pp. 321-336
    • Jongen, H.Th.1    Rückmann, J.-J.2    Stein, O.3
  • 12
    • 0000016156 scopus 로고    scopus 로고
    • Generalized semi-infinite optimization: A first order optimality condition and examples
    • Jongen, H. Th., Rückmann, J.-J. and Stein, O.: Generalized semi-infinite optimization: a first order optimality condition and examples, Math. Programming 83(1) (1998), 145-158.
    • (1998) Math. Programming , vol.83 , Issue.1 , pp. 145-158
    • Jongen, H.Th.1    Rückmann, J.-J.2    Stein, O.3
  • 13
    • 0043031017 scopus 로고
    • Stability of stationary solutions in semi-infinite optimization via the reduction approach
    • W. Oettli and D. Pallaschke (eds), Advances in Optimization, Springer, New York
    • Klatte, D.: Stability of stationary solutions in semi-infinite optimization via the reduction approach, In: W. Oettli and D. Pallaschke (eds), Advances in Optimization, Lecture Notes in Econom. and Math. Systems 382, Springer, New York, 1992.
    • (1992) Lecture Notes in Econom. and Math. Systems , vol.382
    • Klatte, D.1
  • 14
    • 0012696445 scopus 로고
    • Stable local minimizers in semi-infinite optimization: Regularity and second-order conditions
    • Klatte, D.: Stable local minimizers in semi-infinite optimization: regularity and second-order conditions, J. Comput. Appl. Math. 56 (1994), 137-157.
    • (1994) J. Comput. Appl. Math. , vol.56 , pp. 137-157
    • Klatte, D.1
  • 15
    • 0000906253 scopus 로고
    • On time-minimal heating or cooling of a ball
    • Birkhäuser, Basel
    • Krabs, W.: On time-minimal heating or cooling of a ball, In: Internat. Ser. Numer. Math. 81, Birkhäuser, Basel, 1987, pp. 121-131.
    • (1987) Internat. Ser. Numer. Math. , vol.81 , pp. 121-131
    • Krabs, W.1
  • 16
    • 0022076983 scopus 로고
    • On uniqueness of Kuhn-Tucker multipliers in non-linear programming
    • Kyparisis, J.: On uniqueness of Kuhn-Tucker multipliers in non-linear programming, Math. Programming 32 (1985), 242-246.
    • (1985) Math. Programming , vol.32 , pp. 242-246
    • Kyparisis, J.1
  • 17
    • 0019138551 scopus 로고
    • Differential stability in infinite-dimensional nonlinear programming
    • Lempio, F. and Maurer, H.: Differential stability in infinite-dimensional nonlinear programming, Appl. Math. Optim. 6 (1980), 139-152.
    • (1980) Appl. Math. Optim. , vol.6 , pp. 139-152
    • Lempio, F.1    Maurer, H.2
  • 18
    • 0023314734 scopus 로고
    • On the mathematical foundations of nondifferentiable optimization in engineering design
    • Polak, E.: On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Rev. 29 (1987), 21-89.
    • (1987) SIAM Rev. , vol.29 , pp. 21-89
    • Polak, E.1
  • 21
    • 0033239456 scopus 로고    scopus 로고
    • First-order optimality conditions in generalized semi-infinite programming
    • Rückmann, J.-J. and Shapiro, A.: First-order optimality conditions in generalized semi-infinite programming, J. Optim. Theory Appl. 101 (1999), 677-691.
    • (1999) J. Optim. Theory Appl. , vol.101 , pp. 677-691
    • Rückmann, J.-J.1    Shapiro, A.2
  • 22
    • 0022361755 scopus 로고
    • Second-order sensitivity analysis and asymptotic theory of parametrized, nonlinear programs
    • Shapiro, A.: Second-order sensitivity analysis and asymptotic theory of parametrized, nonlinear programs, Math. Programming 33 (1985), 280-299.
    • (1985) Math. Programming , vol.33 , pp. 280-299
    • Shapiro, A.1
  • 23
    • 0000859735 scopus 로고
    • Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton
    • Shapiro, A.: Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton, Appl. Math. Optim. 18 (1988), 215-229.
    • (1988) Appl. Math. Optim. , vol.18 , pp. 215-229
    • Shapiro, A.1
  • 24
    • 0025485978 scopus 로고
    • On concepts of directional differentiability
    • Shapiro, A.: On concepts of directional differentiability, J. Optim. Theory Appl. 66 (1990), 477-487.
    • (1990) J. Optim. Theory Appl. , vol.66 , pp. 477-487
    • Shapiro, A.1
  • 25
    • 0042445825 scopus 로고    scopus 로고
    • Preprint No. 80, RWTH Aachen, Dept. of Mathematics
    • Stein, O.: On level sets of marginal functions, Preprint No. 80, RWTH Aachen, Dept. of Mathematics (C), 1998.
    • (1998) On Level Sets of Marginal Functions , Issue.C
    • Stein, O.1
  • 26
    • 0034348927 scopus 로고    scopus 로고
    • On optimality conditions for generalized semi-infinite programming problems
    • Stein, O. and Still, G.: On optimality conditions for generalized semi-infinite programming problems, J. Optim. Theory Appl. 104 (2000), 443-458.
    • (2000) J. Optim. Theory Appl. , vol.104 , pp. 443-458
    • Stein, O.1    Still, G.2
  • 27
    • 0013534981 scopus 로고    scopus 로고
    • Generalized semi-infinite optimization: On some foundations
    • Weber, G.-W.: Generalized semi-infinite optimization: on some foundations, Vychisl. Tekhnol. 4 (1999), 41-61.
    • (1999) Vychisl. Tekhnol. , vol.4 , pp. 41-61
    • Weber, G.-W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.