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Interior Methods for Mathematical Programs with Complementarity Constraints

Sven Leyffer (leyffer***at***mcs.anl.gov)
Gabriel Lopez-Calva (g-lopez-calva***at***northwestern.edu)
Jorge Nocedal (nocedal***at***ece.northwestern.edu)

Abstract: This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then extended to an interior-relaxation approach. Superlinear convergence to strongly stationary points is also established. Two strategies for updating the penalty parameter are proposed, and their efficiency and robustness are studied on an extensive collection of test problems.

Keywords: MPEC, MPCC, nonlinear programming, interior-point methods, MPEC, MPCC, nonlinear programming, interior-point methods, exact penalty, equilibrium constraints, complementarity constraints

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Complementarity and Variational Inequalities

Citation: Report OTC 2004-10, Northwestern University, Evanston, IL / Preprint ANL/MCS-P1211-1204, Argonne National Laboratory, Argonne, IL, December, 2004

Download: [Postscript][PDF]

Entry Submitted: 12/21/2004
Entry Accepted: 12/21/2004
Entry Last Modified: 07/15/2005

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