Two-Level Optimization Problems with Infinite Number of Convex Lower Level Constraints

This paper proposes a new form of optimization problem which is a two-level programming problem with infinitely many lower level constraints. Firstly, we consider some lower level constraint qualifications (CQs) for this problem. Then, under these CQs, we derive formula for estimating the subdifferential of its valued function. Finally, we present some necessary optimality conditions as Fritz-John type for the problem.