Volume 49, Number 3, July-September 2015
|Page(s)||451 - 472|
|Published online||06 February 2015|
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.
2 LaMOS Research Unit, Operational Research Department, University of Bejaia, 06000 Bejaia, Algeria.
Received: 24 February 2012
Accepted: 1 August 2014
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 (ηi)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 (ηi)i are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.
Mathematics Subject Classification: 26A51 / 90C26 / 90C30 / 90C46
Key words: Nonlinear programming / weak (FJ)-pseudo-invexity / generalized Fritz John condition / generalized Fritz John stationary point / optimality / duality / saddle point
© EDP Sciences, ROADEF, SMAI, 2015
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