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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 4, Pages 173–200 (Mi izv192)  

This article is cited in 9 scientific papers (total in 9 papers)

The subdifferential and the directional derivatives of the maximum of a family of convex functions

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 a family of convex functions under weakened compactness conditions on the indexing set (or in the absence of such conditions).

DOI: https://doi.org/10.4213/im192

Full text: PDF file (2446 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1998, 62:4, 807–832

Bibliographic databases:

MSC: 49J52, 26B05, 46G05, 26A51
Received: 09.09.1996

Citation: V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions”, Izv. RAN. Ser. Mat., 62:4 (1998), 173–200; Izv. Math., 62:4 (1998), 807–832

Citation in format AMSBIB
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\paper The subdifferential and the directional derivatives of the maximum of a~family of convex functions
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\yr 1998
\vol 62
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\pages 173--200
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\pages 807--832
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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. Dinh N., Goberna M.A., Long D.H., Volle M., “Duality For Constrained Robust Sum Optimization Problems”, Math. Program.  crossref  isi
    2. 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  mathnet  crossref  crossref  mathscinet  zmath
    3. Winkler K., “Characterizations of efficient points in convex vector optimization problems”, Mathematical Methods of Operations Research, 53:2 (2001), 205–214  crossref  mathscinet  zmath  isi  elib  scopus
    4. List N., Hush D., Scovel C., Steinwart I., “Gaps in support vector optimization”, Learning Theory, Proceedings, Lecture Notes in Computer Science, 4539, 2007, 336–348  crossref  mathscinet  zmath  isi
    5. 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
    6. Winkler, K, “A CHARACTERIZATION OF EFFICIENT AND WEAKLY EFFICIENT POINTS IN CONVEX VECTOR OPTIMIZATION”, SIAM Journal on Optimization, 19:2 (2008), 756  crossref  mathscinet  zmath  isi  scopus
    7. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet
    8. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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