Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity

Slimani, Hachem; Radjef, Mohammed Said

RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 3, pp. 451-472.

In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different ${\left(\eta {}_i\right)}_i$ assumption. The equivalence between saddle points and optima, and a characterization of optimal solutions are established under suitable generalized invexity requirements. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual. It is shown in this study, with examples, that the introduced generalized Fritz John condition combining with the invexity with respect to different ${\left(\eta {}_i\right)}_i$ are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.

Classification : 26A51, 90C26, 90C30, 90C46
Mots clés : Nonlinear programming, weak (FJ)-pseudo-invexity, generalized Fritz John condition, generalized Fritz John stationary point, optimality, duality, saddle point

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