Séminaire Mathématique de Béjaia
Volume 3, Numéro 1, Pages 13-19
2005-12-31
Generalized V-type I Invexity And Duality For Multiobjective Programs
Authors : Slimani Hachem .
Abstract
As generalization of the invexity notion originated by Hanson [2], Hanson and Mond [3] have introduced type I and type II functions for studying non linear programming problems. Later, Kaul et al. [5], Aghezzaf and Hachimi [1] have defined the notion of type I function with respect to the same function for constrained multiobjective problems. Hanson et al. [4] gave another definition of multiobjective V-type I problem with respect to n . In this paper, following the work of Radjef and Slimani [6], where optimality conditions have been obtained for a nonlinear programming program under invexity with respect to different n_i, we have introduced a, more general, notion of multiobjective V-type I problem with respect to functions ( n_i)_i and (O_j)_j that are not necessarily the same. We have obtained necessary and sufficient conditions for a feasible point to be a weak efficient, efficient or properly efficient solution under various types of generalized V-type I requirements. We have defined a Mond-Weir type dual problem and we have proved weak, strong and converse duality theorems under the defined notions. Known results in the literature [4, 5] can be deduced as particular cases from our results, when the functions ( n_i)_i and (O_j)_j are equal to the same function n which is different to zero.
Keywords
Multiobjective problem, V-type I problem / ( n_i)_i and (O_j)_j ; Quasi-, pseudo-, pseudo quasi-, quasi pseudo- V-type I / ( n_i)_i and (O_j)_j ; Weak, strong and converse duality ; Weak efficient, Efficient, Properly efficient solution.
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