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On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems

Author

Listed:
  • Birbil, S.I.
  • Fang, S-C.
  • Han, J.

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 the proposed algorithm finds an exact solution of VLCP in a finite number of iterations, under some conditions milder than those assumed in literature. Some computational results are included to illustrate the potential of this approach.

Suggested Citation

  • Birbil, S.I. & Fang, S-C. & Han, J., 2002. "On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems," ERIM Report Series Research in Management ERS-2002-72-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:225
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    File URL: https://repub.eur.nl/pub/225/ERS-2002-72-LIS.pdf
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    References listed on IDEAS

    as
    1. James V. Burke & Song Xu, 1998. "The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 719-734, August.
    2. Gowda, M Seetharama & Sznajder, Roman, 1996. "A Generalization of the Nash Equilibrium Theorem on Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 1-12.
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    More about this item

    Keywords

    Newton method; entropy function; finite termination; smoothing approximation; vertical linear complementarity problems;
    All these keywords.

    JEL classification:

    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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