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On the Finite Termination of an Entropy Function Based Non-Interior Continuation Method for Vertical Linear Complementarity Problems |
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| Authors: | |
| Institution: | (1) Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695-7906, USA;(2) Mathematical Sciences and Industrial Engineering, Tsinghua University, Beijing, 100084, P.R. China;(3) Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China;(4) Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, P.R. China;(5) Faculty of Engineering and Natural Sciences, Sabancı University, Orhanli-Tuzla, 34956 Istanbul, Turkey |
| 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. This author’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10271002 and 10401038). This author’s work was partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University. |
| Keywords: | Entropy function Finite termination Non-interior continuation method Vertical linear complementarity problems Smoothing approximation |
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