Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints
The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional constraints are imposed on the control. In this paper we develop three derivation methods for constrained MPEC problems: via concepts from variational analysis, via penalization of the control constraints, and via penalization of the lower-level problem with the subsequent regularization of the resulting nonsmoothness. The developed methods and obtained results are then compared and contrasted.
stationarity conditions control constraints elliptic mathematical programs with equilibrium constraints optimal control of variational inequalities coderivatives 90c33 90c46 49k21 65k10