Probability-one homotopy maps for mixed complementarity problems

Authors:
Kapil Ahuja;Layne T. Watson;Stephen C. Billups
Affiliations:
Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Departments of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061;Department of Mathematical Sciences, University of Colorado at Denver and Health Sciences Center, Denver, USA 80217-3364
Venue:
Computational Optimization and Applications
Year:
2008

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Abstract

Probability-one homotopy algorithms have strong convergence characteristics under mild assumptions. Such algorithms for mixed complementarity problems (MCPs) have potentially wide impact because MCPs are pervasive in science and engineering. A probability-one homotopy algorithm for MCPs was developed earlier by Billups and Watson based on the default homotopy mapping. This algorithm had guaranteed global convergence under some mild conditions, and was able to solve most of the MCPs from the MCPLIB test library. This paper extends that work by presenting some other homotopy mappings, enabling the solution of all the remaining problems from MCPLIB. The homotopy maps employed are the Newton homotopy and homotopy parameter embeddings.