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The Concept of Proper Solution in Linear Programming

Author

Listed:
  • M. G. Fiestras-Janeiro

    (Universidade de Vigo)

  • I. Garcia-Jurado

    (Universidade de Santiago de Compostela)

  • J. Puerto

    (Universidad de Sevilla)

Abstract

In this paper, we study the optimal solutions of a dual pair of linear programming problems that correspond to the proper equilibria of their associated matrix game. We give conditions ensuring the existence of such solutions, show that they are especially robust under perturbation of right-hand-side terms, and describe a procedure to obtain them.

Suggested Citation

  • M. G. Fiestras-Janeiro & I. Garcia-Jurado & J. Puerto, 2000. "The Concept of Proper Solution in Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 511-525, September.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:3:d:10.1023_a:1004601327949
    DOI: 10.1023/A:1004601327949
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    References listed on IDEAS

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    1. Jos A. M. Potters & Stef H. Tijs, 1992. "The Nucleolus of a Matrix Game and Other Nucleoli," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 164-174, February.
    2. Potters, J.A.M. & Tijs, S.H., 1992. "The nucleolus of a matrix game and other nucleoli," Other publications TiSEM ae3402e7-bd19-494b-b0a1-f, Tilburg University, School of Economics and Management.
    3. Stephen M. Robinson, 1977. "A Characterization of Stability in Linear Programming," Operations Research, INFORMS, vol. 25(3), pages 435-447, June.
    4. Fiestras-Janeiro, Gloria & Borm, Peter & van Megen, Freek, 1998. "Protective and Prudent Behaviour in Games," Journal of Economic Theory, Elsevier, vol. 78(1), pages 167-175, January.
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    Citations

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    Cited by:

    1. A. Estévez-Fernández & M.G. Fiestras-Janeiro, 2004. "On Properties of Several Refinements of Optimal Solutions in Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 41-62, July.

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