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

¹ LaMOS Research Unit, Computer Science Department, University of Bejaia, 06000 Bejaia, Algeria.
haslimani@gmail.com
² LaMOS Research Unit, Operational Research Department, University of Bejaia, 06000 Bejaia, Algeria.
radjefms@gmail.com

Received: 24 February 2012
Accepted: 1 August 2014

Abstract

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 (η_i)_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 (η_i)_i are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.