Abstract
In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.
Highlights
The field of multiobjective programming, called vector programming, has grown remarkably in different directions in the settings of optimality conditions and duality theory since the 1980s
Type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential
Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model
Summary
The field of multiobjective programming, called vector programming, has grown remarkably in different directions in the settings of optimality conditions and duality theory since the 1980s It has been enriched by the applications of various types of generalizations of convexity theory, with and without differentiability assumptions. In [11] and [12] some sufficient conditions and duality results were obtained for the new concept of strict minimizer of higher order for a multiobjective optimization problem. The new concepts of invex of order σ ( B,φ ) −V − type II functions are introduced. A sufficient optimality condition is obtained for the nondifferentiable multiobjective programming problem under the new functions and the Wolfe type duality results are obtained
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