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Solving Strongly Monotone Linear Complementarity Problems

Author

Listed:
  • A. CHANDRASHEKARAN

    (School of Mathematics and Computer Science, Central University of Tamil Nadu, Thiruvarur-610 004, Tamil Nadu, India)

  • T. PARTHASARATHY

    (Indian Statistical Institute, Chennai Centre, Chennai - 600 029, Tamil Nadu, India)

  • V. VETRIVEL

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, Tamil Nadu, India)

Abstract

Given a linear transformationLon a finite dimensional real inner product spaceVto itself and an elementq ∈ Vwe consider the general linear complementarity problemLCP(L, K, q)on a proper coneK ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution forLCP(L, K, q), wheneverLis strongly monotone. Lipschitz constants ofLis vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.

Suggested Citation

  • A. Chandrashekaran & T. Parthasarathy & V. Vetrivel, 2013. "Solving Strongly Monotone Linear Complementarity Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-13.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400355
    DOI: 10.1142/S0219198913400355
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    Cited by:

    1. K. C. Sivakumar & M. S. Gowda & G. Ravindran & Usha Mohan, 2020. "Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India," Annals of Operations Research, Springer, vol. 287(2), pages 565-572, April.
    2. G. S. R. Murthy & K. C. Sivakumar & P. Sushmitha, 2020. "T. Parthasarathy’s contributions to complementarity problems: a survey," Annals of Operations Research, Springer, vol. 287(2), pages 867-894, April.

    More about this item

    Keywords

    Complementarity problems; strongly monotone; Lipschitzian property; 22E46; 53C35; 57S20;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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