On Constraint Qualifications for Multiobjective Optimization Problems with Switching Constraints

Abstract

AbstractIn this chapter, we consider multiobjective optimization problems with switching constraint (MOPSC). We introduce linear independence constraint qualification (LICQ), Mangasarian–Fromovitz constraint qualification (MFCQ), Abadie constraint qualification (ACQ), and Guignard constraint qualification (GCQ) for multiobjective optimization problems with switching constraint (MOPSC). Further, we introduce the notion of Weak stationarity, Mordukhovich stationarity, and Strong stationarity, i.e., W-stationarity, M-stationarity, and S-stationarity, respectively, for the MOPSC. Also, we present a survey of the literature related to existing constraint qualifications and stationarity conditions for mathematical programs with equilibrium constraints (MPEC), mathematical programs with complementarity constraints (MPCC), mathematical programs with vanishing constraints (MPVC), and for mathematical programs with switching constraints (MPSC). We establish that the M-stationary conditions are sufficient optimality conditions for the MOPSC using generalized convexity. Further, we propose a Wolfe-type dual model for the MOPSC and establish weak duality and strong duality results under assumptions of generalized convexity.KeywordsSwitching constraintsConstraint qualificationsOptimality conditionsDuality