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On Fully Semimonotone Matrices

Author

Listed:
  • G. S. R. MURTHY

    (Statistical Quality Control and Operations Research, Indian Statistical Institute, Street No. 8, Habsiguda, Hyderabad 500007, Andhra Pradesh, India)

  • T. PARTHASARATHY

    (Indian Statistical Institute, 37/110, Nelson Manicham Road, Chennai 600029, Tamil Nadu, India)

  • R. SRIDHAR

    (Information Analytics, PD & GT, Caterpillar Inc, Peoria IL 61629, USA)

Abstract

The class of fully semimonotone matrices is well known in the study of the linear complementarity problem. Stone [(1981) Ph.D. thesis, Dept. of Operations Research, Stanford University, Stanford, CA] introduced this class and conjectured that the principal minors of any fully semimonotoneQ0-matrix are non-negative. While the problem is still open, Murthy and Parthasarathy [(1998)Math. Program.82, 401–411] introduced the concept of incidence using which they proved that the principal minors of any matrix in the class of fully copositiveQ0-matrices, a subclass of fully semimonotoneQ0-matrices, are non-negative. In this paper, we study some properties of fully semimonotone matrices in connection with incidence. The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence. We also present an interesting characterization ofQ0for matrices with a special structure. This result is very useful in checking whether a given matrix belongs toQ0provided it has the special structure. Several examples are discussed in connection with incidence andQ0property.

Suggested Citation

  • G. S. R. Murthy & T. Parthasarathy & R. Sridhar, 2013. "On Fully Semimonotone Matrices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-17.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400367
    DOI: 10.1142/S0219198913400367
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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.

    More about this item

    Keywords

    Linear complementarity problem; fully semimonotone matrices; complementary cones; incidence; 90C33;
    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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