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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 1, Pages 107–132 (Mi izv323)  

This article is cited in 8 scientific papers (total in 8 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.

DOI: https://doi.org/10.4213/im323

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English version:
Izvestiya: Mathematics, 2001, 65:1, 99–121

Bibliographic databases:

MSC: 49J52, 26B05, 26B25, 46G05, 26A51
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. RAN. Ser. Mat., 65:1 (2001), 107–132; Izv. Math., 65:1 (2001), 99–121

Citation in format AMSBIB
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\by V.~N.~Solov'ev
\paper The subdifferential and the directional derivatives of the maximum of a~family of convex functions.~II
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 107--132
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\crossref{https://doi.org/10.4213/im323}
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\zmath{https://zbmath.org/?q=an:1017.49020}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 99--121
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000323}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747103818}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hantoute, A, “A Complete Characterization of the Subdifferential Set of the Supremum of an Arbitrary Family of Convex Functions”, Journal of Convex Analysis, 15:4 (2008), 831  mathscinet  zmath  isi
    2. Hantoute, A, “SUBDIFFERENTIAL CALCULUS RULES IN CONVEX ANALYSIS: A UNIFYING APPROACH VIA POINTWISE SUPREMUM FUNCTIONS”, SIAM Journal on Optimization, 19:2 (2008), 863  crossref  mathscinet  zmath  isi  scopus
    3. Chong Li, K. F. Ng, “Subdifferential Calculus Rules for Supremum Functions in Convex Analysis”, SIAM J. Optim, 21:3 (2011), 782  crossref  mathscinet  zmath  isi  scopus
    4. Yu. S. Ledyaev, J. S. Treiman, “Sub- and supergradients of envelopes, semicontinuous closures, and limits of sequences of functions”, Russian Math. Surveys, 67:2 (2012), 345–373  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Correa R., Hantoute A., Lopez M.A., “Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions”, SIAM J. Optim., 26:4 (2016), 2219–2234  crossref  mathscinet  zmath  isi  scopus
    6. Li M. Wang Ch. Qu B., “Non-Convex Semi-Infinite Min-Max Optimization With Noncompact Sets”, J. Ind. Manag. Optim., 13:4 (2017), 1859–1881  crossref  mathscinet  zmath  isi  scopus
    7. Correa R., Hantoute A., Lopez M.A., “Valadier-Like Formulas For the Supremum Function i”, J. Convex Anal., 25:4 (2018), 1253–1278  mathscinet  zmath  isi
    8. Correa R., Hantoute A., Lopez-Cerda M.A., “Moreau-Rockafellar-Type Formulas For the Subdifferential of the Supremum Function”, SIAM J. Optim., 29:2 (2019), 1106–1130  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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