The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions
und | 21. Sept. 2017
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Online veröffentlicht: 21. Sept. 2017
Seitenbereich: 39 - 48
Eingereicht: 27. Mai 2016
Akzeptiert: 29. Juni 2016
DOI: https://doi.org/10.1515/auom-2017-0019
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© 2017
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 conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed.