Mordukhovich Normal Cone of Optimization Problems with Switching Constraints
نویسندگان
1 Department of Mathematics, University of Payame Noor (PNU), P.O. Box 19395-4697, Tehran, Iran.
2 Department of Mathematics, University of Payame Noor (PNU), P.O. Box 19395-4697, Tehran, Iran.
doi
10.30473/coam.2024.70234.1251چکیده
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.
