Literature cited
R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).
D. P. Bertsekas and S. K. Mitter, “A descent numerical method for optimization problems with nondifferentiable cost functionals,” SIAM J. Control.,11, No. 4, 637–652 (1973).
C. Lemarechal, “An algorithm for minimizing convex functions,” in: Information Processing 74, Proc. of IFIP Congress 74, North-Holland, Amsterdam (1974), pp. 552–556.
C. Lemarechal, “Méthodes de sous-gradients,” Bull. Direction Études Recherches Sér. C. Math. Informat., No. 2, 5–14 (1974).
Ya. I. Zabotin, A. I. Korablev, and R. F. Khabibullin, “On the minimization of quasi-convex functionals,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 27–33 (1972).
Ya. I. Zabotin, A. I. Korablev, and R. F. Khabibullin, “Conditions for the extremum of a functional in the presence of constraints,” Kibernetika, No. 6, 65–70 (1973).
H. H. Schaefer, Topology Vector Spaces, Macmillan, New York (1966).
A. I. Korablev and O. V. Mironov, “The minimization of a pseudoconvex maximum function by the ɛ-subgradient method,” in: Abstracts of the Communications at the Conference of Young Scientists on Radiospectroscopy, Quantum Acoustics, Mechanics, and Applied Mathematics, Kazan (1978), pp. 105–106.
V. F. Dem'yanov and V. N. Malozemov, Introduction to Minimax [in Russian], Nauka, Moscow (1972).
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Translated from Issledovaniya po Prikladnoi Matematike, No. 7, pp. 3–11, 1979.
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Korablev, A.I. ɛ-Subgradient method for the solution of nonlinear extremal problems. J Math Sci 43, 2419–2425 (1988). https://doi.org/10.1007/BF01095644
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DOI: https://doi.org/10.1007/BF01095644