<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed. </p></abstract>

In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed.

The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker...

The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions

Publié en ligne: 21 sept. 2017

Pages: 39 - 48

Reçu: 27 mai 2016

Accepté: 29 juin 2016

DOI: https://doi.org/10.1515/auom-2017-0019

Mots clés
Generalized Algebraic Operations, Generalized Gradient, Farkas Lemma, Karush-Kuhn-Tucker Conditions, Lagrange Multipliers

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions

Publié en ligne: 21 sept. 2017

Pages: 39 - 48

Reçu: 27 mai 2016

Accepté: 29 juin 2016

DOI: https://doi.org/10.1515/auom-2017-0019

Mots clésGeneralized Algebraic Operations, Generalized Gradient, Farkas Lemma, Karush-Kuhn-Tucker Conditions, Lagrange Multipliers

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Generalized Algebraic Operations, Generalized Gradient, Farkas Lemma, Karush-Kuhn-Tucker Conditions, Lagrange Multipliers