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

Slimani, Hachem; Radjef, Mohammed Said

doi:10.1051/ro/2014046

Slimani, Hachem ¹ ; Radjef, Mohammed Said ²

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.

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

Résumé

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.

Reçu le : 2012-02-24
Accepté le : 2014-08-01

MR Zbl

DOI : 10.1051/ro/2014046

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

Affiliations des auteurs :

Slimani, Hachem ¹ ; Radjef, Mohammed Said ²

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.

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     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://www.numdam.org/articles/10.1051/ro/2014046/}
}

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

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