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Stein Linear Programs Over Symmetric Cones

Author

Listed:
  • I. JEYARAMAN

    (The Institute of Mathematical Sciences, Chennai - 600 113, India)

  • K. C. SIVAKUMAR

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

  • V. VETRIVEL

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

Abstract

In this paper, using Moore–Penrose inverse, we characterize the feasibility of primal and dual Stein linear programs over symmetric cones in a Euclidean Jordan algebraV. We give sufficient conditions for the solvability of the Stein linear programming problem. Further, we give a characterization of the globally uniquely solvable property for the Stein transformation in terms of a least element of a set inVin the context of the linear complementarity problem.

Suggested Citation

  • I. Jeyaraman & K. C. Sivakumar & V. Vetrivel, 2013. "Stein Linear Programs Over Symmetric Cones," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-14.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400331
    DOI: 10.1142/S0219198913400331
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    References listed on IDEAS

    as
    1. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    More about this item

    Keywords

    Stein linear programming; Euclidean Jordan algebra; symmetric cone; Moore–Penrose inverse; least element; complementarity problem; GUS-property; 90C05; 90C25; 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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