Abstract
In this paper, we investigate the properties of the optimal solutions obtained when we translate the concepts of perfect, proper, and weakly proper solutions from the context of linear complementarity to the framework of linear programming.
Similar content being viewed by others
References
Mohan, S. R., and Talman, A. J. J., Refinement of Solutions to the Linear Complementarity Problem, Tilburg University, Center for Economic Research, Discussion Paper 9878, 1998.
Selten, R., Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory, Vol. 4. pp. 25–55, 1975.
Myerson, R., Refinements of the Nash Equilibrium Concept, International Journal of Game Theory, Vol. 7, pp. 73–80, 1978.
van Damme, E., Stability and Perfection of Nash Equilibrium, Springer-Verlag, New York, NY 1991.
Fiestras-Janeiro, M.G., García-Jurado, I., and Puerto, J., The Concept of Proper Solutions in Linear Programming, Journal of Optimization Theory and Applications, Vol. 106, pp. 511–525, 2000.
Potters, J., and Tijs, S., The Nucleolus of a Matrix Game and Other Nucleoli, Mathematics of Operations Research, Vol. 17, pp. 164–174, 1992.
Marchi, E., and Oviedo, J.A., Lexicographic Optimality in the Multiple-Objective Linear Programming: The Nucleolar Solution, European Journal of Operational Research, Vol. 57, pp. 355–359, 1992.
Mangasarian, O.L., Simplified Characterizations of Linear Complementarity Problems Solvable as Linear Programs, Mathematics of Operations Research, Vol. 4. pp. 268–273, 1979
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Estévez-Fernández, A., Fiestras-Janeiro, M. On Properties of Several Refinements of Optimal Solutions in Linear Programming. Journal of Optimization Theory and Applications 122, 41–62 (2004). https://doi.org/10.1023/B:JOTA.0000041730.73603.54
Issue Date:
DOI: https://doi.org/10.1023/B:JOTA.0000041730.73603.54