Abstract
The main existence and uniqueness theorem of Part 1 is applied to three specific problems, namely, (a) the symmetric, dual, nonlinear programs of Dantzig, Eisenberg, and Cottle, (b) the saddle point problem of a differentiable scalar function over an unbounded product set, and (c) the equilibrium point problem of ann-person game.
Similar content being viewed by others
References
Karamardian, S.,The Nonlinear Complementarity Problem with Applications, Part 1, Journal of Optimization Theory and Applications, Vol. 4, No. 2, 1969.
Dantzig, G. B., Eisenberg, E., andCottle, R. W.,Symmetric Dual Nonlinear Programs, University of California at Berkeley, Operations Research Center, Report No. 30 IER 172–35, 1962.
Cottle, R. W.,Nonlinear Programs with Positively Bounded Jacobians, SIAM Journal on Applied Mathematics, Vol. 14, No. 1, 1966.
Wolfe, P.,A Duality Theorem for Nonlinear Programming, Quarterly of Applied Mathematics, Vol. 19, No. 3, 1962.
Kortanek, K., andJeroslow, R.,A Note on Some Classical Methods in Constrained Optimization and Positively Bounded Jacobian, Operations Research, Vol. 19, No. 5, 1967.
Cottle, R. W.,Comments on the Note by Kortanek and Jeroslow, Operations Research, Vol. 19, No. 5, 1967.
Sion, M.,On General Minimax Theorems, Pacific Journal of Mathematics, Vol. 8, No. 1, 1958.
Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, 1951.
Nash, J. F.,Equilibrium Points in n-Person Games, Proceedings of the National Academy of Sciences, Vol. 36, No. 1, 1950.
Arrow, K. J., andDebreu, G.,Existence of an Equilibrium for a Competitive Economy, Econometrica, Vol. 22, No. 3, 1954.
McKenzie, L. W.,On the Existence of General Equilibrium for a Competitive Market, Econometrica, Vol. 27, No. 1, 1959.
Rosen, J. B.,Existence and Uniqueness of Equilibrium Points for Concave n-Person Games, Econometrica, Vol. 22, No. 3, 1965.
Author information
Authors and Affiliations
Additional information
The author is very grateful to the referee for his many helpful comments on an earlier version of the paper.
Rights and permissions
About this article
Cite this article
Karamardian, S. The nonlinear complementarity problem with applications, part 2. J Optim Theory Appl 4, 167–181 (1969). https://doi.org/10.1007/BF00930577
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00930577