References
V. F. Dem'yanov and V. N. Malozemov, An Introduction to Minmax [in Russian], Nauka, Moscow (1972).
V. V. Fedorov, Numerical Maxmin Methods [in Russian], Nauka, Moscow (1979).
E. A. Nurminskii, Numerical Methods for Solving Deterministic and Stochastic Minmax Problems [in Russian], Naukova Dumka, Kiev (1979).
Yu. M. Ermol'ev and A. A. Gaivoronskii, “A stochastic method for solving minmax problems,” Kibernetika, No. 4, 92–97 (1983).
A. A. Gaivoronskii, “Numerical methods for minimization of convex functionals of probability measures with application to optimal monitoring,” Kibernetika, No. 4, 43–51 (1989).
S. V. Shibaev, “A method of finding the minmax of functionals dependent on probability measures,” Kibern. Sistem. Anal., No. 2, 79–85 (1992).
V. V. Fedorov, Optimal Experiment Theory [in Russian], Nauka, Moscow (1971).
H. Moulin, Game Theory for the Social Sciences, NYU Press, New York (1982).
S. V. Shibaev, Analysis of Substantive Scenarios of Player Behavior Under Incomplete Information [in Russian], abstract of thesis, Inst. Kibern. Akad. Nauk Ukr., Kiev (1988).
S. V. Shibaev, “Stochastic maxmin algorithm,” in: Mathematical Methods of Analysis of Complex Stochastic Systems, Inst. Kibern. Akad. Nauk Ukr., Kiev (1988), pp. 12–17.
Yu. M. Ermol'ev, Stochastic Programming Methods [in Russian], Nauka, Moscow (1976).
E. G. Gol'shtein and N. V. Tret'yakov, “Weakly augmented Lagrange functions and associated duality theorems,” Ekon. Mat. Metody,15, No. 6, 1180–1193 (1979).
R. T. Rockafellar, “Augmented Lagrangians and applications of the proximal point algorithm in convex programming,” Math. Oper. Res., No. 1, 97–116 (1980).
H. Uzawa, “Iterative methods in convex programming,” in: Studies in Linear and Nonlinear Programming [Russian translations], IL, Moscow (1962).
W. I. Zangwill, Nonlinear Programming: A Unified Approach, Prentice Hall, Englewood Cliffs, N.J. (1969).
Yu. M. Ermol'ev “Methods for solving nonlinear extremal problems,” Kibernetika, No. 4, 1–17 (1966).
E. G. Gol'shtein, “Generalized gradient method for finding saddle points,” Ekon. Mat. Metody,8, No. 4, 569–579 (1972).
E. A. Nurminskii and P. I. Verchenko, “Convergence of saddle-point algorithms,” Kibernetika, No. 3, 112–116 (1977).
G. D. Maistrovskii, “On gradient saddle-point methods,” Ekon. Mat. Metody,12, No. 5, 917–929 (1976).
V. F. Dem'yanov, “Subgradient method and saddle points,” Vestnik LGU, No. 7, 17–23 (1981).
A. S. Nemirovskii and D. B. Yudin, “Cesare convergence of the gradient method for approximation of saddle points of convex — concave functions,” Dokl. Akad. Nauk SSSR,239, No. 5, 1056–1059 (1978).
Yu. M. Ermol'ev and E. A. Nurminskii, “Limit extremal problems,” Kibernetika, No. 4, 130–132 (1973).
A. M. Gupal and A. N. Golodnikov, “Some methods of solving limit extremal problems,” in: Methods of Operations Research and Reliability Theory in System Analysis [in Russian], (1976), pp. 64–74.
E. A. Nurminskii and A. A. Gaivoronskii, “Nonstationary extremal problem,” in: Methods of Operations Research and Reliability Theory in System Analysis [in Russian], (1976), pp. 84–97.
F. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York (1983).
K. Parthasarathy, An Introduction to Probability Theory and Measure Theory [Russian translation], Mir, Moscow (1983).
B. N. Pshenichnyi, Necessary Conditions of Extremum [in Russian], Nauka, Moscow (1982).
S. P. Uryas'ev, “Step control for direct stochastic programming methods,” Kibernetika, No. 6, 96–98 (1979).
S. V. Shibaev, “A stochastic method for solving constrained minmax problems,” in: Mathematical Methods of Analysis and Optimization of Complex Systems Operating Under Uncertainty [in Russian], Inst. Kibern. Akad. Nauk Ukr, Kiev (1989), pp. 10–17.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 103–114, November–December, 1994.
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Shibaev, S.V. Maxmin subject to marginal constraints. Cybern Syst Anal 30, 875–884 (1994). https://doi.org/10.1007/BF02366446
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DOI: https://doi.org/10.1007/BF02366446