Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 9 2 2024 12 01 Mordukhovich Normal Cone of Optimization Problems with Switching Constraints 85 96 11075 10.30473/coam.2024.70234.1251 EN Sharifeh Rezagholi Department of Mathematics, University of Payame Noor (PNU), P.O. Box 19395-4697, Tehran, Iran. Arash Farhadi Hikooee‎ Department of Mathematics, University of Payame Noor (PNU), P.O. Box 19395-4697, Tehran, Iran. Journal Article 2024 01 17 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. https://mathco.journals.pnu.ac.ir/article_11075_ca54183d00b111c64ddca62fbd0e6338.pdf