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Exact penalization of mathematical programs with equilibrium constraints. (English) Zbl 0922.90128

Summary: We study theoretical and computational aspects of an exact penalization approach to mathematical programs with equilibrium constraints (MPECs). In the first part, we prove that a Mangasarian-Fromovitz-type condition ensures the existence of a stable local error bound at the root of a real-valued nonnegative piecewise smooth function. A specification to nonsmooth formulations of equilibrium constraints, e.g., complementarity conditions or normal equations, provides conditions which guarantee the existence of a nonsmooth exact penalty function for MPECs. In the second part, we study a trust region minimization method for a class of composite nonsmooth functions which comprises exact penalty functions arising from MPECs. We prove a global convergence result for the general method and incorporate a penalty update rule. A further specification results in an SQP trust region method for MPECs based on an \(\ell_1\) penalty function.

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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