Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
نویسندگان
چکیده
We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weirtype dual problems for our nonsmooth multiobjective problems and establish duality theorems for weak Pareto-optimal solutions under generalized convexity assumptions and regularity conditions.
منابع مشابه
Nonsmooth Multiobjective Fractional Programming with Generalized Invexity
In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...
متن کاملOptimality and Duality for an Efficient Solution of Multiobjective Nonlinear Fractional Programming Problem Involving Semilocally Convex Functions
In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...
متن کاملBenson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality
In this paper, we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints. We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions. We also fo...
متن کاملSufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{I}$-type-I univexity over cones
In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...
متن کاملOptimality and duality for nonsmooth multiobjective fractional programming with mixed constraints
We consider nonsmooth multiobjective fractional programming problems with inequality and equality constraints. We establish the necessary and sufficient optimality conditions under various generalized invexity assumptions. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems.
متن کامل