Partial exact penalty for mathematical programs with equilibrium constraints
A new approach to mathematical programming with equilibrium constraints (MPEC) is proposed based on the result of partial exact penalization. An algorithm for computing the M-stationary point of MPEC without linear independence constraint qualification is elaborated. The nonsmoothness of the partial exact function is the main difficulty. The authors overcome it by smoothing the partial exact penalty function, obtaining a smooth optimization problem with simple linear complementarity non-negative constraints. Although the subproblem is still an MPEC, the complementarity constraint is simple and the linear independence constraint qualification holds at all feasible points. This makes the problem solvable by existing algorithms for finding S-stationary points. The smoothing algorithm proposed in this paper takes the smoothing parameter to zero and adjusts the partial exact penalty parameter. Its behaviour is similar to other penalty algorithms, since the accumulation point may not be feasible. However, it is proved that if the accumulation point satisfies an extended version of MPEC with general Mangasarian-Fromovitz constraint qualification then it is a Mordukhovich-stationary point.
mathematical program with equilibrium constraints
Mangasarian-Fromovitz constraint qualification
scientific article; zbMATH DE number 5529269