Séminaire Mathématique de Béjaia
Volume 5, Numéro 1, Pages 21-27
2007-12-31
Nondifferentiable Multiobjective Programming Under Generalized D_i-invexity
Authors : Slimani Hachem .
Abstract
We are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We define new class of nondifferentiable functions called dI-invexity in which each component of the objective function is directionally differentiable in its own direction dj. In the following, from Suneja and Srivastava [6], Mishra and Noor [3], Slimani and Radjef [5], we introduce new classes of problems called dI-V-type I, quasi-, pseudo-, pseudo quasi-, quasi pseudo- dI-V-type I with respect to (ηj)j and (Oj)j. In the framework of the new concepts, we prove new Fritz-John type necessary and Karush-Kuhn-Tucker type necessary and sufficient optimality conditions for a feasible point to be weakly efficient or efficient solution. Moreover, we prove weak and strong duality results for Mond-Weir type dual under various types of generalized dI-V-type I requirements.
Keywords
Nondifferentiable multiobjective programming ; Optimality ; Duality ; Directional derivative ; dI-invexity ; dI-V-type I ; Weakly efficient, Efficient and Properly efficient solution.
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