Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems

In this paper, we obtain characterizations of solution sets of the interval-valued mathematical programming problems with switching constraints. Stationary conditions which are weaker than the standard Karush-Kuhn-Tucker conditions need to be discussed in order to find the necessary optimality conditions. We introduce corresponding weak, Mordukhovich, and strong stationary conditions for the corresponding interval-valued mathematical programming problems with switching constraints (IVPSC) and interval-valued tightened nonlinear problems (IVTNP), because the W-stationary condition of IVPSC is equivalent to Karush-Kuhn-Tucker conditions of the IVTNP. Furthermore, we use strong stationary conditions to characterize the several solutions sets for IVTNP, in which the last ones are particular solutions sets for IVPSC at the same time, because the feasible set of tightened nonlinear problems (IVTNP) is a subset of the feasible set of the mathematical programs with switching constraints (IVPSC).