Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

Izhar Ahmad

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DOI: 10.4236/am.2011.24057                

Abstract

In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.

Keywords

Multiobjective Programming, Nondifferentiable Programming, Generalized dI-Univexity, Sufficiency, Duality

Conflicts of Interest

The authors declare no conflicts of interest.

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