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Interior-point method for nonlinear programming with complementarity constraints

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cs.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: In this report, we propose an algorithm for solving nonlinear programming problems with com-plementarity constraints, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We use an exact penalty function to remove complementarity constraints. Thus a new indefinite linear system is defined with a tridiagonal low-right submatrix. Inexact solution of this system is obtained iteratively using indefinitely preconditioned conjugate gradient method. Furthermore, new merit function is defined, which includes barrier, exact penalty, and augmented Lagrangian terms. The algorithm was implemented in the interactive system for universal functional optimization UFO. Results of extensive numerical experiments are reported.

Keywords: Nonlinear programming, complementarity constraints, interior-point methods, indefinite systems, indefinite preconditioners, preconditioned conjugate gradient method, merit functions, algorithms, computational experiments.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical report No. 1039, Institute of Computer Sciencer, Pod Vodarenskou Vezi 2, 18207 Praha 8, December 2008.

Download: [Postscript][PDF]

Entry Submitted: 02/25/2009
Entry Accepted: 02/25/2009
Entry Last Modified: 02/25/2009

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