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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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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.

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Authors and Affiliations

  1. Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC, 27695-7906, USA

    Shu-Cherng Fang

  2. Mathematical Sciences and Industrial Engineering, Tsinghua University, Beijing, 100084, P.R. China

    Shu-Cherng Fang

  3. Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Jiye Han

  4. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, P.R. China

    Zheng-Hai Huang

  5. Faculty of Engineering and Natural Sciences, Sabancı University, Orhanli-Tuzla, 34956, Istanbul, Turkey

    Ş. İlker Bİrbİl

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  1. Shu-Cherng Fang
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  2. Jiye Han
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  4. Ş. İlker Bİrbİl
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Correspondence to Shu-Cherng Fang.

Additional information

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.

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Fang, SC., Han, J., Huang, ZH. et al. On the Finite Termination of an Entropy Function Based Non-Interior Continuation Method for Vertical Linear Complementarity Problems. J Glob Optim 33, 369–391 (2005). https://doi.org/10.1007/s10898-004-6098-5

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  • DOI: https://doi.org/10.1007/s10898-004-6098-5

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