Séminaire Mathématique de Béjaia
Volume 4, Numéro 1, Pages 15-21
2006-12-31
Duality For Nonlinear Programming Under Invexity With Respect To Different ηi
Authors : Slimani Hachem .
Abstract
In [6, 8], Radjef and Slimani are considered the invexity and its extensions for objective and constraint functions with respect to different i. Optimality conditions, for nonlinear and multiobjective programming problems, are obtained under this generalized invexity. In [7], for multiobjective programming, some duality results are obtained for a dual in the format of Mond-Weir under generalized V-type I invexity with respect to different ( i)i and (0 ) . Further, in [6, 7, 8], a generalized Kuhn-Tucker relation is introduced which is necessary and sufficient for a feasible point to be optimal under various types of generalized invexity requirements. Numerical examples are constructed and show that the results obtained in [6, 7, 8] are applicable to prove that a feasible point is optimal when this point is not Kuhn-Tucker stationary (resp. a vector Kuhn-Tucker) for a nonlinear (resp. multiobjective) programming problem. In this paper, following the work given in [6] and using the generalized Kuhn-Tucker relation, two dual programs in the format of Wolfe and Mond-Weir are considered. Weak, strong, converse and strict duality results are obtained, for each dual programme, under the defined generalized invexity assumptions.
Keywords
Nonlinear programming ; KT-invexity with respect to η and (\theta_j)_j; KT-pseudo-invexity with respect to η and (\theta_j)_j ; Generalized Kuhn-Tucker relation; Weak, strong, converse and strict duality ; Optimal solution.
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