Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T08:55:01.046Z Has data issue: false hasContentIssue false

On nonlinear programming and matrix game equivalence

Published online by Cambridge University Press:  17 February 2009

Vasile Preda
Affiliation:
Mathematics Faculty, University of Bucharest, 14, Academiei Street, Bucharest, România
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the framework of Mond-Weir duality a new equivalence between nonlinear programming and a matrix game is given. Finally, certain conclusions about convex programming with nested maxima and matrix games are also included.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Chandra, S., Craven, B. D. and Mond, B., “Generalized concavity and duality with a square root term”, Optimization 16 (1985) 653662.Google Scholar
[2]Chandra, S., Craven, B. D. and Mond, B., “Non-linear programming duality and matrix game equivalence”, J. Austral. Math. Soc. Ser. B 26 (1985) 422429.CrossRefGoogle Scholar
[3]Dantzig, G. B., “A proof of the equivalence of the programming problem and the game problem”, in Activity analysis of production and allocation (ed. Koopmans, T. C.), Cowles Commission Monograph No. 13, (John Wiley and Sons, 1951).Google Scholar
[4]Karlin, S., Mathematical methods and theory in games, programming and mathematical economics (Addison-Wesley, Reading, Mass., 1959).Google Scholar
[5]Kemp, M. and Kimura, Y., Introduction to mathematical economics (Springer Verlag, New York, 1978).Google Scholar
[6]Kortanek, K. O. and Evans, J. P., “Pseudo-concave programming and convex Lagrange regularity”, Oper. Res. 15 (1967) 882891.Google Scholar
[7]Mond, B. and Weir, T., “Generalized concavity and duality”, in Generalized concavity in optimization and economics (eds. Schaible, S. and Ziemba, W. T.), (Academic Press, 1981), 263279.Google Scholar
[8]Preda, V., “Convex optimization with nested maxima and matrix game equivalence”, Annals of Bucharest University 3 (1989) 5760.Google Scholar
[9]Scott, C. H., Jefferson, T. R. and Sirri, E., “On duality for convex minimization with nested maxima”, J. Austral. Math. Soc. Ser. B 26 (1985) 517522.Google Scholar