Well Posedness of New Optimization Problems with Variational Inequality Constraints

Abstract

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

Keywords

• well posedness
• constrained variational control problem
• monotonicity
• pseudomonotonicity
• hemicontinuity
• multiple integral functional