Abstract
The paper suggests a method for finding the minimax of functionals dependent on probability measures. Almost sure convergence of the method is proved. The method is applied to optimal experimental design problems.
Similar content being viewed by others
Literature Cited
V. V. Fedorov, Optimal Experiment Theory [in Russian], Nauka, Moscow (1971).
H. Moulin, Game Theory with Examples from Mathematical Economics [Russian translation], Mir, Moscow (1985).
A. A. Gaivoronskii, "Numerical minimization methods for convex functionals of probability measures with applications to optimal monitoring," Kibernetika, No. 4, 43–51 (1989).
Yu. M. Ermol'ev and A. A. Gaivoronskii, "Stochastic method for solving minimax problems," Kibernetika, No. 4, 92–97 (1983).
R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).
E. G. Gladyshev, "On stochastic approximation," Teor. Veroyatn. Ee Primen.,10, No. 2, 297–300 (1965).
F. R. Gantmakher, Matrix Theory [in Russian], Nauka, Moscow (1988).
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 79–85, March–April, 1992.
Rights and permissions
About this article
Cite this article
Shibaev, S.V. A method to find the minimax of functionals dependent on probability measures. Cybern Syst Anal 28, 227–232 (1992). https://doi.org/10.1007/BF01126209
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01126209