Mordukhovich Normal Cone of Optimization Problems with Switching Constraints

Rezagholi, Sharifeh; Farhadi Hikooee‎, Arash

doi:10.30473/coam.2024.70234.1251

Document Type : Research Article

Authors

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

https://doi.org/10.30473/coam.2024.70234.1251

Abstract

This paper examines normal cones of the feasible set for mathematical programming problems with switching constraints (MPSC)‎. ‎Functions involved are assumed to be continuously differentiable‎. ‎The primary focus is on providing the upper estimate of the Mordukhovich normal cone for the feasible set of MPSCs‎. ‎First‎, ‎a constraint qualification‎, ‎called the ``MPSC-No Nonzero Abnormal Multiplier Constraint Qualification''‎, ‎is considered for the problem‎. ‎Based on this qualification‎, ‎the main result of the paper is presented‎. ‎Finally‎, ‎an optimality condition‎, ‎called the ``necessary M-stationarity condition'' is proposed for optimal solutions of the considered problems‎. ‎Since other optimization problems with multiplicative constraints can be rewritten in the form of MPSCs‎, ‎results obtained in this paper can be extended to a wider class of problems involving multiplicative constraints‎.

Keywords

Main Subjects

Control and Optimization

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Mordukhovich Normal Cone of Optimization Problems with Switching Constraints

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Volume 9, Issue 2 Open Access PolicyDecember 2024Pages 85-96

Volume 9, Issue 2
Open Access Policy
December 2024
Pages 85-96