A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems

Authors:
Tecla De Luca;Francisco Facchinei;Christian Kanzow
Affiliations:
Fondazione Ugo Bordoni, Via Baldassarre Castiglione 59, I-00142 Roma, Italy. tdeluca@fub.it;Università di Roma “La Sapienza”, Dipartimento di Informatica e Sistemistica, Via Buonarroti 12, I-00185 Roma, Italy. soler@dis.uniroma1.it;University of Hamburg, Institute of Applied Mathematics, Bundesstrasse 55, D-20146 Hamburg, Germany. kanzow@math.uni-hamburg.de
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

In this paper we introduce a general line search scheme which easily allows us to define and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a search direction to be used in the general scheme has to enjoy in order to guarantee global convergence, local superlinear/quadratic convergence or finite convergence. We examine in detail several different semismooth algorithms and compare their theoretical features and their practical behavior on a set of large-scale problems.