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Volumn 44, Issue 4, 1998, Pages 327-350

Necessary conditions for extremality and separation theorems with applications to multiobjective optimization

Author keywords

Efficiency; Ekeland's variational principle; Extremality; Local compactness; Multiobjective programming; Separation theorems; Subdifferentials

Indexed keywords


EID: 0012317922     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939808844416     Document Type: Article
Times cited : (12)

References (37)
  • 1
    • 0021375867 scopus 로고
    • Lipschitz behavior of solutions to nonconvex problem
    • Aubin, J. P. (1984). Lipschitz behavior of solutions to nonconvex problem, Math. Oper. Res., 9, 87-111.
    • (1984) Math. Oper. Res. , vol.9 , pp. 87-111
    • Aubin, J.P.1
  • 2
    • 0002820799 scopus 로고
    • Proper efficient points for maximization with respect to cones
    • Borwein, J. M. (1977). Proper efficient points for maximization with respect to cones, SIAM J. Control Optim., 15, 57-63.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 57-63
    • Borwein, J.M.1
  • 3
    • 38249036307 scopus 로고
    • Epi-Lipschitz-like sets in Banach space: Theorems and examples
    • Borwein, J. M. (1987). Epi-Lipschitz-like sets in Banach space: theorems and examples, Nonlinear Anal. Th. Meth. Appl., 11, 1207-1217.
    • (1987) Nonlinear Anal. Th. Meth. Appl. , vol.11 , pp. 1207-1217
    • Borwein, J.M.1
  • 5
    • 0024035435 scopus 로고
    • Optimality conditions for maximations of set-valued functions
    • Corley, H. W. (1988). Optimality conditions for maximations of set-valued functions, J. Optim. Th. Appl., 58, 1-10.
    • (1988) J. Optim. Th. Appl. , vol.58 , pp. 1-10
    • Corley, H.W.1
  • 6
    • 0023422065 scopus 로고
    • Existence and Lagrangian duality for maximization of set-valued functions
    • Corley, H. W. (1987). Existence and Lagrangian duality for maximization of set-valued functions, J. Optim. Th. Appl., 54, 489-501.
    • (1987) J. Optim. Th. Appl. , vol.54 , pp. 489-501
    • Corley, H.W.1
  • 7
    • 0024304380 scopus 로고
    • Nonsmooth multiobjective programming
    • Craven, B. D. (1989). Nonsmooth multiobjective programming, Numer. Funct. Anal. Optim., 10, 65-76.
    • (1989) Numer. Funct. Anal. Optim. , vol.10 , pp. 65-76
    • Craven, B.D.1
  • 8
    • 0002117178 scopus 로고
    • General duality in vector optimization
    • Dolecki, S. and Malivert, C. (1993). General duality in vector optimization, Optimization, 27, 97-119.
    • (1993) Optimization , vol.27 , pp. 97-119
    • Dolecki, S.1    Malivert, C.2
  • 9
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland, I. (1974). On the variational principle, J. Math. Anal. Appl., 47, 324-353.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 324-353
    • Ekeland, I.1
  • 11
    • 0000879867 scopus 로고
    • Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces
    • El Abdouni, B. and Thibault, L. (1992). Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces, Optimization, 26, 277-285.
    • (1992) Optimization , vol.26 , pp. 277-285
    • El Abdouni, B.1    Thibault, L.2
  • 12
    • 0025517021 scopus 로고
    • Nonconvex separation theorems and some applications in vector optimization
    • Gerth, C. and Weidner, P. (1990). Nonconvex separation theorems and some applications in vector optimization, J. Optim. Th. Appl., 67, 297-320.
    • (1990) J. Optim. Th. Appl. , vol.67 , pp. 297-320
    • Gerth, C.1    Weidner, P.2
  • 13
    • 84967717450 scopus 로고
    • Approximate subdifferentials and applications 1: The finite dimensional theory
    • Ioffe, A. D. (1984). Approximate subdifferentials and applications 1: The finite dimensional theory, Trans. Amer. Math. Soc., 281, 289-316.
    • (1984) Trans. Amer. Math. Soc. , vol.281 , pp. 289-316
    • Ioffe, A.D.1
  • 14
    • 84974312624 scopus 로고
    • Approximate subdifferentials and applications 2: Functions on locally convex spaces'
    • Ioffe, A. D. (1986). Approximate subdifferentials and applications 2: Functions on locally convex spaces', Mathematika, 33, 111-128.
    • (1986) Mathematika , vol.33 , pp. 111-128
    • Ioffe, A.D.1
  • 15
    • 84966259071 scopus 로고
    • Approximate subdifferentials and applications 3: Metric theory
    • Ioffe, A. D. (1989). Approximate subdifferentials and applications 3: Metric theory, Mathematika, 36, 1-38.
    • (1989) Mathematika , vol.36 , pp. 1-38
    • Ioffe, A.D.1
  • 16
    • 84960582452 scopus 로고
    • Proximal analysis and approximate subdifferentials
    • Ioffe, A. D. (1990). Proximal analysis and approximate subdifferentials, J. London Math. Soc., 41, 175-192.
    • (1990) J. London Math. Soc. , vol.41 , pp. 175-192
    • Ioffe, A.D.1
  • 18
    • 0021449669 scopus 로고
    • Scalarization in vector optimization
    • Jahn, J. (1984). Scalarization in vector optimization, Math. Prog., 29, 203-218.
    • (1984) Math. Prog. , vol.29 , pp. 203-218
    • Jahn, J.1
  • 19
    • 0028480697 scopus 로고
    • Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
    • Jourani, A. (1994). Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems, Math. Prog., 66, 1-23.
    • (1994) Math. Prog. , vol.66 , pp. 1-23
    • Jourani, A.1
  • 20
    • 0038328483 scopus 로고
    • Compactly epi-Lipschitzian sets and A-subdifferential in WT-spaces
    • Jourani, A. (1995). Compactly epi-Lipschitzian sets and A-subdifferential in WT-spaces, Optimization, 34, 1-17.
    • (1995) Optimization , vol.34 , pp. 1-17
    • Jourani, A.1
  • 21
    • 84966242235 scopus 로고
    • Verifiable conditions for openness and metric regularity of multivalued mappings in Banach spaces
    • Jourani, A. and Thibault, L. (1995). Verifiable conditions for openness and metric regularity of multivalued mappings in Banach spaces, Tran. Amer. Math. Soc., 347, 1255-1268.
    • (1995) Tran. Amer. Math. Soc. , vol.347 , pp. 1255-1268
    • Jourani, A.1    Thibault, L.2
  • 22
    • 0030496625 scopus 로고    scopus 로고
    • Extensions of subdifferential calculus rules in Banach spaces and applications
    • Jourani, A. and Thibault, L. (1996). Extensions of subdifferential calculus rules in Banach spaces and applications, Can. J. Math., 48, 834-848.
    • (1996) Can. J. Math. , vol.48 , pp. 834-848
    • Jourani, A.1    Thibault, L.2
  • 23
    • 85034178028 scopus 로고    scopus 로고
    • Coderivatives of multivalued mappings, locally compact cones and metric regularity
    • to appear
    • Jourani, A. and Thibault, L. (1996). Coderivatives of multivalued mappings, locally compact cones and metric regularity, Nonlinear Anal. Th. Meth. Appl., to appear.
    • (1996) Nonlinear Anal. Th. Meth. Appl.
    • Jourani, A.1    Thibault, L.2
  • 24
    • 0010877032 scopus 로고
    • A covering theorem for set-valued mappings
    • Kruger, A. Ya. (1988). A covering theorem for set-valued mappings, Optimization, 19, 763-780.
    • (1988) Optimization , vol.19 , pp. 763-780
    • Kruger, A.Ya.1
  • 26
    • 0000259921 scopus 로고
    • Extreme points and the Euler equations in nondifferentiable optimization problems
    • Kruger, A. Ya. and Mordukhovich, B. S. (1980). Extreme points and the Euler equations in nondifferentiable optimization problems, Dokl. Akad., Nauk BSSR, 24, 684-687.
    • (1980) Dokl. Akad., Nauk BSSR , vol.24 , pp. 684-687
    • Kruger, A.Ya.1    Mordukhovich, B.S.2
  • 27
    • 0017994125 scopus 로고
    • Minimization of nonsmooth functionals in optimal control problems
    • Kruger, A. Ya. and Mordukhovich, B. S. (1978). Minimization of nonsmooth functionals in optimal control problems, Engrg. Cybern., 16, 126-133.
    • (1978) Engrg. Cybern. , vol.16 , pp. 126-133
    • Kruger, A.Ya.1    Mordukhovich, B.S.2
  • 28
    • 0001442538 scopus 로고
    • Limits of Fréchet normals in nonsmooth analysis, Optimization and nonlinear analysis
    • Eds. Ioffe, A., Marcus, M. and Reich, S.
    • Loewen, P. D. (1990). Limits of Fréchet normals in nonsmooth analysis, Optimization and nonlinear analysis, Eds. Ioffe, A., Marcus, M. and Reich, S., Pitman Research Notes in Mathematics Series.
    • (1990) Pitman Research Notes in Mathematics Series
    • Loewen, P.D.1
  • 30
    • 0020845963 scopus 로고
    • Weak-Pareto optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space
    • Minami, M. (1983). Weak-Pareto optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space, J. Optim. Th. Appl., 41, 451-461.
    • (1983) J. Optim. Th. Appl. , vol.41 , pp. 451-461
    • Minami, M.1
  • 31
    • 0001657279 scopus 로고    scopus 로고
    • Extremal characterization of Asplund spaces
    • Mordukhovich, D. S. and Shao, Y. (1996). Extremal characterization of Asplund spaces, Proc. Amer. Math. Soc., 124. 197-205.
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 197-205
    • Mordukhovich, D.S.1    Shao, Y.2
  • 33
    • 0040383360 scopus 로고
    • Invexity in multifunction optimization
    • Sach, P. H. and Craven, B. D. (1991). Invexity in multifunction optimization, Numer. Funct. Anal. Optim., 12, 383-394.
    • (1991) Numer. Funct. Anal. Optim. , vol.12 , pp. 383-394
    • Sach, P.H.1    Craven, B.D.2
  • 35
    • 85034164620 scopus 로고
    • Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems, Optimization and nonlinear analysis
    • Eds. Ioffe, A., Marcus, M. and Reich, S.
    • Thibault, L. (1990). Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems, Optimization and nonlinear analysis, Eds. Ioffe, A., Marcus, M. and Reich, S., Pitman Research Notes in Mathematics Series.
    • (1990) Pitman Research Notes in Mathematics Series
    • Thibault, L.1
  • 36
    • 0003030229 scopus 로고    scopus 로고
    • Integration of subdifferentials of lower semicontinuous functions in Banach spaces
    • Thibault, L. and Zagrodny, D., Integration of subdifferentials of lower semicontinuous functions in Banach spaces, J. Math. Anal. Appl., 189, 33-58.
    • J. Math. Anal. Appl. , vol.189 , pp. 33-58
    • Thibault, L.1    Zagrodny, D.2
  • 37
    • 26444612793 scopus 로고
    • On the characterization of efficient points by mean of monotone functionals
    • Weidner, P. (1988). On the characterization of efficient points by mean of monotone functionals, Optimization, 19, 53-69.
    • (1988) Optimization , vol.19 , pp. 53-69
    • Weidner, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.