Exact penalization of mathematical programs with equilibrium constraints

Exact penalization of mathematical programs with equilibrium constraints

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Article ID: iaor20011535
Country: United States
Volume: 37
Issue: 2
Start Page Number: 617
End Page Number: 652
Publication Date: Feb 1999
Journal: SIAM Journal on Control and Optimization
Authors: ,
Keywords: penalty functions
Abstract:

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 L1 penalty function.

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