An Interior Point Method for Mathematical Programs with Complementarity Constraints (MPCCs)

Arvind U. Raghunathan (aurandrew.cmu.edu)
Lorenz T. Biegler (lb01andrew.cmu.edu)

Abstract: Interior point methods for nonlinear programs (NLPs) are adapted for solution of mathematical programs with complementarity constraints (MPCCs). The constraints of the MPCC are suitably relaxed so as to guarantee a strictly feasible interior for the inequality constraints. The standard primal-dual algorithm has been adapted with a modified step calculation. The algorithm is shown to be superlinearly convergent in the neighborhood of the solution set under assumptions of MPCC-LICQ, strong stationarity and upper level strict complementarity. The modification can be easily accommodated within most nonlinear programming interior point algorithms with identical local behavior. Numerical experience is also presented and holds promise for the proposed method.

Keywords: Nonlinear programming, Interior point method, MPEC, MPCC

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Complementarity and Variational Inequalities

Citation: SIAM J. on Optimization, 15(3):720-750 (2005)

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Entry Submitted: 06/10/2003
Entry Accepted: 06/10/2003
Entry Last Modified: 07/09/2005

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