Abstract
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-Weir-type dual problems for our nonsmooth multiobjective problems and establish duality theorems for (weak) Pareto-optimal solutions under generalized convexity assumptions and regularity conditions.
Highlights
Multiobjective programming problems arise when more than one objective function is to be optimized over a given feasible region
Majumdar gave sufficient optimality conditions for differentiable multiobjective programming which modified those given in Singh under the assumption of convexity, pseudoconvexity, and quasiconvexity of the functions involved at the Pareto-optimal solution
We introduce nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions for inequality and equality constraints
Summary
Multiobjective programming problems arise when more than one objective function is to be optimized over a given feasible region. Majumdar gave sufficient optimality conditions for differentiable multiobjective programming which modified those given in Singh under the assumption of convexity, pseudoconvexity, and quasiconvexity of the functions involved at the Pareto-optimal solution. Journal of Inequalities and Applications nonsmooth multiobjective programming problems involving locally Lipschitz functions for inequality and equality constraints. They extended sufficient optimality conditions in Kim et al 13 to the nonsmooth case and established duality theorems for nonsmooth multiobjective programming problems involving locally Lipschitz functions. We introduce nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions for inequality and equality constraints. We propose a Wolfe-type dual and a Mond-Weir-type dual for the primal problem and establish duality results between the primal problem and its dual problems under generalized convexity and regularity conditions
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