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Volumn 23, Issue 7-8, 2002, Pages 807-831

Generalized contingent epiderivatives in set-valued optimization: Optimality conditions

Author keywords

Aubin property; Contingent cone; Generalized contingent epiderivative; Lagrange multipliers; Optimality conditions; Regularity conditions; Set valued optimization

Indexed keywords

BOUNDARY CONDITIONS; CONFORMAL MAPPING; CONSTRAINT THEORY; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); GRAPH THEORY; LAGRANGE MULTIPLIERS; SET THEORY; THEOREM PROVING;

EID: 0036868452     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1081/NFA-120016271     Document Type: Article
Times cited : (59)

References (34)
  • 1
    • 0003086078 scopus 로고
    • Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions
    • Nachbin, L., Ed.
    • Aubin, J.P. Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions. In Advances in Mathematics, Supplementary studies; Nachbin, L., Ed.; 1981; 159-229.
    • (1981) Advances in Mathematics, Supplementary Studies , pp. 159-229
    • Aubin, J.P.1
  • 3
    • 0033246218 scopus 로고    scopus 로고
    • On subdifferentials of set-valued maps
    • Baier, J.; Jahn, J. On Subdifferentials of Set-Valued Maps. J. Optim. Theory Appl. 1999, 100, 233-240.
    • (1999) J. Optim. Theory Appl. , vol.100 , pp. 233-240
    • Baier, J.1    Jahn, J.2
  • 4
    • 0016048964 scopus 로고
    • On the cones of tangents with applications to mathematical programming
    • Bazaraa, M.S.; Goode, J.J.; Nashed, M.Z. On the Cones of Tangents with Applications to Mathematical Programming. J. Optim. Theory Appl. 1974, 13, 389-426.
    • (1974) J. Optim. Theory Appl. , vol.13 , pp. 389-426
    • Bazaraa, M.S.1    Goode, J.J.2    Nashed, M.Z.3
  • 5
    • 0002820799 scopus 로고
    • Proper efficient points for maximizations with respect to cones
    • Borwein, J. Proper Efficient Points for Maximizations with Respect to Cones. SIAM J. Control Optim. 1977, 15, 57-63.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 57-63
    • Borwein, J.1
  • 6
    • 0032356083 scopus 로고    scopus 로고
    • Contingent epiderivative and its applications to set-valued optimization
    • Bernarczuk, E.M.; Song, W. Contingent Epiderivative and Its Applications to Set-Valued Optimization. Control Cybern. 1998, 27, 375-386.
    • (1998) Control Cybern. , vol.27 , pp. 375-386
    • Bernarczuk, E.M.1    Song, W.2
  • 8
    • 0000061469 scopus 로고    scopus 로고
    • Optimality conditions for set-valued optimization problems
    • Chen, G.Y.; Jahn, J. Optimality Conditions for Set-Valued Optimization Problems. Math. Meth. Oper. Res. 1998, 48, 187-200.
    • (1998) Math. Meth. Oper. Res. , vol.48 , pp. 187-200
    • Chen, G.Y.1    Jahn, J.2
  • 9
    • 0024035435 scopus 로고
    • Optimality conditions for maximization of set-valued functions
    • Corley, H.W. Optimality Conditions for Maximization of Set-Valued Functions, J. Optim. Theory Appl. 1988, 58, 1-10.
    • (1988) J. Optim. Theory Appl. , vol.58 , pp. 1-10
    • Corley, H.W.1
  • 11
    • 0000544715 scopus 로고    scopus 로고
    • Optimality conditions for problems with set-valued objectives
    • El Abdouni, B.; Thibault, L. Optimality Conditions for Problems with Set-Valued Objectives. J. Appl. Anal. 1996, 2, 183-201.
    • (1996) J. Appl. Anal. , vol.2 , pp. 183-201
    • El Abdouni, B.1    Thibault, L.2
  • 12
    • 0034905140 scopus 로고    scopus 로고
    • Optimality conditions in non-convex set-valued optimization
    • Flores-Bazan, F. Optimality Conditions in Non-convex Set-Valued Optimization. Math. Meth. Oper. Res. 2001, 53, 403-417.
    • (2001) Math. Meth. Oper. Res. , vol.53 , pp. 403-417
    • Flores-Bazan, F.1
  • 13
    • 0025517021 scopus 로고
    • Nonconvex separation theorems and some applications in vector optimization
    • Gerth, C.; Weidner, P. Nonconvex Separation Theorems and Some Applications in Vector Optimization. J. Optim. Theory Appl. 1990, 67, 297-320.
    • (1990) J. Optim. Theory Appl. , vol.67 , pp. 297-320
    • Gerth, C.1    Weidner, P.2
  • 14
    • 0023453959 scopus 로고
    • Theorems of the alternative for multifunctions with applications to optimization: General results
    • Giannessi, F. Theorems of the Alternative for Multifunctions with Applications to Optimization: General results. J. Optim. Theory Appl. 1987, 55, 233-256.
    • (1987) J. Optim. Theory Appl. , vol.55 , pp. 233-256
    • Giannessi, F.1
  • 15
    • 17444448069 scopus 로고    scopus 로고
    • The lagrange multiplier rule in set-valued optimization
    • Götz, A.; Jahn, J. The Lagrange Multiplier Rule in Set-Valued Optimization, SIAM J. On Optim. 1999, 10, 331-344.
    • (1999) SIAM J. On Optim. , vol.10 , pp. 331-344
    • Götz, A.1    Jahn, J.2
  • 16
    • 0022128359 scopus 로고
    • A characterization of properly minimal elements of a set
    • Jahn, J. A Characterization of Properly Minimal Elements of a Set. SIAM J. Control Optim. 1985, 23, 649-656.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 649-656
    • Jahn, J.1
  • 19
    • 0012335570 scopus 로고    scopus 로고
    • Existence theorems and characterizations of generalized contingent epiderivatives
    • Jahn, J.; Khan, A.A. Existence Theorems and Characterizations of Generalized Contingent Epiderivatives. To Appear in: J. Nonl. Convex Anal.
    • J. Nonl. Convex Anal.
    • Jahn, J.1    Khan, A.A.2
  • 20
    • 0031383054 scopus 로고    scopus 로고
    • Contingent epiderivatives and set-valued optimization
    • Jahn, J.; Rauh, R. Contingent Epiderivatives and Set-Valued Optimization. Math. Meth. Oper. Res. 1997, 46, 193-211.
    • (1997) Math. Meth. Oper. Res. , vol.46 , pp. 193-211
    • Jahn, J.1    Rauh, R.2
  • 21
    • 0022675326 scopus 로고
    • Generalized quasiconvex mappings and vector optimization
    • Jahn, J.; Sachs, E. Generalized Quasiconvex Mappings and Vector Optimization. SIAM J. Control Optim. 1986, 24, 306-322.
    • (1986) SIAM J. Control Optim. , vol.24 , pp. 306-322
    • Jahn, J.1    Sachs, E.2
  • 22
    • 0012317922 scopus 로고    scopus 로고
    • Necessary conditions for extremality and separation theorems with applications to multiobjective optimization
    • Jourani, A. Necessary Conditions for Extremality and Separation Theorems with Applications to Multiobjective Optimization. Optimization 1998, 44, 327-350.
    • (1998) Optimization , vol.44 , pp. 327-350
    • Jourani, A.1
  • 23
    • 0017001951 scopus 로고
    • On the existence and nonexistence of lagrange multipliers in banach spaces
    • Kurcyusz, S. On the Existence and Nonexistence of Lagrange Multipliers in Banach spaces. J. Optim. Theory Appl. 1976, 20, 81-110.
    • (1976) J. Optim. Theory Appl. , vol.20 , pp. 81-110
    • Kurcyusz, S.1
  • 24
    • 21244446300 scopus 로고    scopus 로고
    • Differential and sensitivity properties of gap functions for vector variational inequalities
    • Li, S.J.; Yan, H.; Chen, G.Y. Differential and Sensitivity Properties of Gap Functions for Vector Variational Inequalities. To appear in: Math. Meth. Oper. Res.
    • Math. Meth. Oper. Res.
    • Li, S.J.1    Yan, H.2    Chen, G.Y.3
  • 26
    • 0343773004 scopus 로고    scopus 로고
    • On cone characterizations of weak, proper and pareto optimality in multiobjective optimization
    • Miettinen, K.; Mäkelä, M.M. On Cone Characterizations of Weak, Proper and Pareto Optimality in Multiobjective Optimization. Math. Meth. Oper. Res. 2001, 53, 233-245.
    • (2001) Math. Meth. Oper. Res. , vol.53 , pp. 233-245
    • Miettinen, K.1    Mäkelä, M.M.2
  • 27
    • 84966206068 scopus 로고
    • Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis
    • Mordukhovich, B. Stability Theory for Parametric Generalized Equations and Variational Inequalities via Nonsmooth Analysis. Trans. Amer. Math. Soc. 1994, 343, 609-657.
    • (1994) Trans. Amer. Math. Soc. , vol.343 , pp. 609-657
    • Mordukhovich, B.1
  • 28
    • 0020166855 scopus 로고
    • On regularity conditions in mathematical programming
    • Penot, J.P. On Regularity Conditions in Mathematical Programming. Math. Program. Study 1982, 19, 167-199.
    • (1982) Math. Program. Study , vol.19 , pp. 167-199
    • Penot, J.P.1
  • 29
    • 0016993914 scopus 로고
    • Stability theory for systems of inequalities. II: Differentiable nonlinear systems
    • Robinson, S.M. Stability Theory for Systems of Inequalities. II: Differentiable Nonlinear Systems. SIAM J. Numer. Anal. 1976, 13, 497-513.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 31
    • 0031998275 scopus 로고    scopus 로고
    • Set-valued derivatives of multifunctions and optimality conditions
    • Taa, A. Set-Valued Derivatives of Multifunctions and Optimality Conditions, Numer. Funct. Anal. Optim. 1998, 19, 121-140.
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 121-140
    • Taa, A.1
  • 32
    • 0024001849 scopus 로고
    • Stability and sensitivity analysis in convex vector optimization
    • Tanino, T. Stability and Sensitivity Analysis in Convex Vector Optimization. SIAM J. Control Optim. 1988, 26, 521-536.
    • (1988) SIAM J. Control Optim. , vol.26 , pp. 521-536
    • Tanino, T.1
  • 33
    • 0036113892 scopus 로고    scopus 로고
    • On relations between vector optimization problems and vector variational inequalities
    • Ward, D.E.; Lee, G.M. On Relations Between Vector Optimization Problems and Vector Variational Inequalities. J. Optim. Theory Appl. 2002, 113, 583-596.
    • (2002) J. Optim. Theory Appl. , vol.113 , pp. 583-596
    • Ward, D.E.1    Lee, G.M.2
  • 34
    • 0002800189 scopus 로고
    • Regularity and stability for the mathematical programming problem in banachspaces
    • Zowe, J.; Kurcyusz, S. Regularity and Stability for the Mathematical Programming Problem in Banachspaces. Appl. Math. Optim. 1979, 5, 49-62.
    • (1979) Appl. Math. Optim. , vol.5 , pp. 49-62
    • Zowe, J.1    Kurcyusz, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.