Optimality and duality for multiobjective programming involving subdifferentiable set functions

Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be suficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. Duality results are thus extended for a Wolfe-type or a Mond-Weir type dual.

[1]  C. R. Bector,et al.  Duality for Multiobjective Fractional Programming Involving n-Set Functions , 1994 .

[2]  Second order optimality conditions for mathematical prograramming with set functions , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[3]  Hang-Chin Lai,et al.  The Fenchel-Moreau theorem for set functions , 1988 .

[4]  G. J. Zalmai.  Optimality conditions and duality for multiobjective measurable subset selection problems , 1991 .

[5]  H. Lai,et al.  Saddle point and duality in the optimization theory of convex set functions , 1982, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[6]  P. Wolfe.  A duality theorem for non-linear programming , 1961 .

[7]  Gue Myung Lee,et al.  Duality for multiobjective programming involving n-set functions , 1994 .

[8]  G. J. Zalmai,et al.  Sufficiency criteria and duality for nonlinear programs involving n-set functions , 1990 .

[9]  H. W. Corley,et al.  Existence and Lagrangian duality for maximizations of set-valued functions , 1987 .

[10]  C. R. Bector,et al.  Efficiency and Duality for Nonlinear Multiobjective Programs Involving n-Set Functions , 1994 .

[11]  Lai-Jiu Lin,et al.  Moreau-Rockafellar Type Theorem for Convex Set Functions* , 1988 .

[12]  H. W. Corley,et al.  Optimization Theory for n-Set Functions , 1987 .

[13]  Robert J. T. Morris,et al.  Optimal constrained selection of a measurable subset , 1979 .

[14]  Lai-Jiu Lin.  Optimization of Set-Valued Functions , 1994 .

[15]  S. Sinha.  A Duality Theorem for Nonlinear Programming , 1966 .

[16]  Lai-Jiu Lin,et al.  On the optimality of differentiable nonconvex n-set functions☆ , 1992 .

[17]  G. J. Zalmai.  Duality for generalized fractional programs involving n-set functions , 1990 .

[18]  Tan-Yu Lee,et al.  Lagrange multiplier theorem of multiobjective programming problems with set functions , 1991 .

[19]  Lai-Jiu Lin,et al.  On the optimality conditions of vector-valued n-set functions☆ , 1991 .

[20]  H. Lai,et al.  Duality in mathematical programming of set functions: On Fenchel duality theorem , 1983 .