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.

Accepted:

DOI: 10.1051/ro/2014046

Keywords: Nonlinear programming, weak (FJ)-pseudo-invexity, generalized Fritz John condition, generalized Fritz John stationary point, optimality, duality, saddle point

^{1}; Radjef, Mohammed Said

^{2}

@article{RO_2015__49_3_451_0, author = {Slimani, Hachem and Radjef, Mohammed Said}, title = {Fritz {John} type optimality and duality in nonlinear programming under weak pseudo-invexity}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {451--472}, publisher = {EDP-Sciences}, volume = {49}, number = {3}, year = {2015}, doi = {10.1051/ro/2014046}, mrnumber = {3349129}, zbl = {1338.90326}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2014046/} }

TY - JOUR AU - Slimani, Hachem AU - Radjef, Mohammed Said TI - Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 451 EP - 472 VL - 49 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2014046/ DO - 10.1051/ro/2014046 LA - en ID - RO_2015__49_3_451_0 ER -

%0 Journal Article %A Slimani, Hachem %A Radjef, Mohammed Said %T Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 451-472 %V 49 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2014046/ %R 10.1051/ro/2014046 %G en %F RO_2015__49_3_451_0

Slimani, Hachem; Radjef, Mohammed Said. Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity. RAIRO - Operations Research - Recherche Opérationnelle, Volume 49 (2015) no. 3, pp. 451-472. doi : 10.1051/ro/2014046. http://archive.numdam.org/articles/10.1051/ro/2014046/

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