Some Properties of Regularization and Penalization Schemes for MPECs

Daniel Ralph (danny.ralphjims.cam.ac.uk)
Stephen J. Wright (swrightcs.wisc.edu)

Abstract: Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In the penalized formulation, the complementarity constraint appears as a penalty term in the objective. Existence and uniqueness of solutions for these formulations are investigated, and estimates are obtained for the distance of these solutions to the MPEC solution under various assumptions.

Keywords: Nonlinear Programming, Equilibrium Constraints, Complementarity Constraints

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Complementarity and Variational Inequalities

Citation: Optimization Technical Report 03-04, December 2003, Computer Sciences Department, University of Wisconsin-Madison. Revised April, 2004

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Entry Submitted: 12/11/2003
Entry Accepted: 12/11/2003
Entry Last Modified: 04/09/2004

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