Guignard Qualifications and Stationary Conditions for Mathematical Programming with Nonsmooth Switching Constraints

Gorgini Shabankareh, Fatemeh; Kanzi, Nader; Izadi, Javad; Fallahi, Kamal

doi:10.30473/coam.2021.60747.1176

Document Type : Research Article

Authors

Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran

https://doi.org/10.30473/coam.2021.60747.1176

Abstract

In this paper‎, ‎some constraint qualifications ‎of‎ the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints‎. ‎Then‎, ‎a new type of stationary condition‎, ‎named parametric stationary condition‎, ‎is presented for the problem‎, ‎and it is shown that all the stationarity conditions in various papers can be deduced from it‎. ‎This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case‎. ‎Finally‎, ‎the article ends with two important examples‎. ‎The results of the article are formulated according to Clark subdifferential and using nonsmooth analysis methods.

Keywords

References

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Guignard Qualifications and Stationary Conditions for Mathematical Programming with Nonsmooth Switching Constraints

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References

Volume 6, Issue 2 Open Access PolicySummer-Autumn 2021July 2021Pages 23-35

Volume 6, Issue 2
Open Access Policy
Summer-Autumn 2021
July 2021
Pages 23-35