On the Finite Termination of an Entropy Function Based Non-Interior Continuation Method for Vertical Linear Complementarity Problems

Authors:
Shu-Cherng Fang;Jiye Han;Zheng-Hai Huang;Ş. İlker Birbil
Affiliations:
Aff1 Aff2;Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, P.R. China 100080;Department of Mathematics, School of Science, Tianjin University, Tianjin, P.R. China 300072;Faculty of Engineering and Natural Sciences, Sabancı University, Istanbul, Turkey 34956
Venue:
Journal of Global Optimization
Year:
2005

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Abstract

By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that under some milder than usual assumptions the proposed algorithm finds an exact solution of VLCP in a finite number of iterations. Some computational results are included to illustrate the potential of this approach.