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This article is cited in 11 scientific papers (total in 11 papers)
The subdifferential and the directional derivatives of the maximum of a family of convex functions. II
V. N. Solov'ev M. V. Lomonosov Moscow State University
Abstract:
The paper deals with calculating the directional derivatives and the subdifferential of the maximum of convex functions with no compactness conditions on the indexing set. We apply our results to the problems of minimax theory in which the Lagrange function is not assumed to be concave. We also apply these results to the duality theory of non-convex extremum problems, and strengthen earlier results of Yakubovich, Matveev and the author. We illustrate our results by investigating a problem of optimal design of experiments.
Received: 29.09.1999
Citation:
V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions. II”, Izv. Math., 65:1 (2001), 99–121
Linking options:
https://www.mathnet.ru/eng/im323https://doi.org/10.1070/im2001v065n01ABEH000323 https://www.mathnet.ru/eng/im/v65/i1/p107
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