Equilibrium problems with equilibrium constraints via multiobjective optimization

This article concerns a new class of optimization-related problems called equilibrium problems with equilibrium constraints (SPEC). One may treat them as two-level hierarchical problems, which involve equilibria at both lower and upper levels. Such problems naturally appear in various applications providing an equilibrium counterpart (at the upper level) of mathematical programs with equilibrium constraints (MPEC). We develop a unified approach to both EPECs and MPECs from the viewpoint of multiobjective optimization subject to equilibrium constraints. The problems of this type are intrinsically nonsmooth and require the use of generalized differentiation for their analysis and applications. This article presents necessary optimality conditions for EPECs in finite-dimensional spaces based on advanced generalized differential tools of variational analysis. The optimality conditions are derived in normal form under certain qualification requirements, which can be regarded as proper analogs of the classical Mangasarian-Fromovitz constraint qualification in the general settings under consideration.