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

References

• Aubin , J.P. 1984 . Lipschitz behavior of solutions to nonconvex problem . Math, Oper. Res , 9 : 87 – 111 .
   Web of Science ®Google Scholar
• Borwein , J.M. 1977 . Proper efficient points of maximization with respect to cones . SIAM J. Control Optim , 15 : 57 – 63 .
   Web of Science ®Google Scholar
• Borwein , J.M. 1987 . Epi-Lipschiz-like sets in Banach space: theorems and examples . Nonlinear Anal. Th. Meth. Appl , 11 : 1207 – 1217 .
   Web of Science ®Google Scholar
• Clarke , F.H. 1983 . Optimization and nonsmooth analysis , New York : Wiley-interscience .
   Google Scholar
• Corley , H.W. 1988 . Optimality conditions for maximations of set-valued functions . J. Optim. Th. Appl , 58 : 1 – 10 .
   Web of Science ®Google Scholar
• Corley , H.W. 1987 . Existence and Lagruangian duality of maximization of setvalued functions . J. Optim. Th. Appl , 54 : 489 – 501 .
   Web of Science ®Google Scholar
• Craven , B.D. 1989 . Nonsmooth multiobjective programming . Numer. Funct. Anal. Optim , 10 : 65 – 76 .
   Google Scholar
• Dolecki , S. and Malivert , C. 1993 . General duality in vector optimization . Optimization , 27 : 97 – 119 .
   Google Scholar
• Ekeland , I. 1974 . On the variational principle . J. Math. Anal. Appl , 47 : 324 – 353 .
   Web of Science ®Google Scholar
• El Abdouni , B. 1994 . “ Contributions à l'optimisation multivoque etàl analyse non linéaire ” . In Thèse d état , Rabat, , Morocco : Université Mohamed V .
   Google Scholar
• El Abdouni , B. and Thibault , L. 1992 . Lagrange multipliers for Pareto nonsmooth programming porblems in Banach spaces . Optimization , 26 : 277 – 285 .
   Google Scholar
• Gerth , C. and Weidner , P. 1990 . Nonconvex separation theorems and some applications in vector optimization . J. Optim. Th. Appl , 67 : 297 – 320 .
   Web of Science ®Google Scholar
• Ioffe , A.D. 1984 . Approximate subdifferentials and applications 1: The finite dimensional theory . Trans. Amer. Math. Soc , 281 : 289 – 316 .
   Google Scholar
• Ioffe , A.D. 1986 . Approximate subdifferentials and applications 2: Functions on locally convex spaces . Mathematika , 33 : 111 – 128 .
   Google Scholar
• Ioffe , A.D. 1989 . Approximate subdifferentials and applications 3: Metrie theory . Mathematika , 36 : 1 – 38 .
   Google Scholar
• Ioffe , A.D. 1990 . Proximal analysis and approximate subdifferentials . J. London Math. Soc , 41 : 175 – 192 .
   Web of Science ®Google Scholar
• Jahn , J. 1986 . Mathematical vector optimization in partially order linear spaces Lang Frankfurt
   Google Scholar
• Jahn , J. 1984 . Scalarization in vector optimization . Math. Prog , 29 : 203 – 218 .
   Web of Science ®Google Scholar
• Jourani , A. 1994 . Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems . Math. Prog , 66 : 1 – 23 .
   Web of Science ®Google Scholar
• Jourani , A. 1995 . Compactly epi-Lipschizian sets and A-subdifferential in WT-spaces . Optimization , 34 : 1 – 17 .
   Google Scholar
• 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 .
   Google Scholar
• Jourani , A. and Thibault , L. 1996 . Extensions of subdifferential calculus rules in Banach spaces and applications . Can. J. Math , 48 : 834 – 848 .
   Google Scholar
• Jourani A. Thibault L. Coderivatives of multivalued mappings. locally compact cones and metric regularity Nonlinear Anal. Th. Meth. Appl. 1996 to appear
   Google Scholar
• Kruger , Ya A. 1988 . A covering theorem for set-valued mappings . Optimization , 19 : 763 – 780 .
   Google Scholar
• Kruger , Ya A. 1977 . Subdifferential of nonconvex functions and generalized directional derivatives Minsk
   Google Scholar
• Kruger , A.Ya. and Mordukhovich , B.S. 1980 . Extreme points and the eEuler equations in nondifferentiable optimization problems . Dokl. Akad. Nauk. BBSSR , 24 : 684 – 687 .
   Web of Science ®Google Scholar
• Kruger , A.Ya. and Mordukhovich , B.S. 1978 . Minimization of nonsmooth functionals in optimal control problems . Engrg. Cybern , 16 : 126 – 133 .
   Google Scholar
• Loewen , P.D. 1990 . Limits of Fréchet normals in nonsmooth analysis, Optimixation and nonlinear analysis , Edited by: Loffe , A. , Marcus , M. and Reich , S. Pitman Research Notes in Mathematics Series .
   Google Scholar
• Luc , D.T. 1989 . Theory of vector optimization , Springer-Verlag .
   Google Scholar
• Minami , M. 1983 . Weak-Pareto optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space . J. Optim. Th. Appl , 41 : 451 – 461 .
   Web of Science ®Google Scholar
• Mordukhovich , B.S. and Shao , Y. 1996 . Extremal characterization of Asplund spaces . Proc. Amer. Matn. Soc , 124 : 197 – 205 .
   Google Scholar
• Rockafellar , R.T. 1985 . Lipschitz property on multifuncations . Nonlin. Anal. Th. Meth. Appl , 9 : 867 – 885 .
   Web of Science ®Google Scholar
• Sach , P.H. and Craven , B.D. 1991 . Invexity in multifunction optimization . Numer. Funct. Anal. Optim , 12 : 383 – 394 .
   Web of Science ®Google Scholar
• Sach , P.H. and Craven , B.D. 1991 . Invex multifunctions and duality . Numer, Funct. Anal. Optim , 12 : 575 – 591 .
   Web of Science ®Google Scholar
• Thibault , L. 1990 . Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems, Optimization and nonlinear analysis Edited by: Ioffe , A. , Marcus , M. and Reich , S. Pitman Research Notes in Mathematics Series
   Google Scholar
• Thibault , L. and Zagrodny , D. 1990 . Intergration of subdifferentials of lower semincontinuous functions in Banach spaces . J. Math. Anal. Appl , 189 : 33 – 58 .
   Google Scholar
• Weidner , P. 1988 . On the characterization of efficient points by mean of monotone functionals . Optimization , 19 : 53 – 69 .
   Google Scholar