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Variational Geometric Approach to Generalized Differential and Conjugate Calculi in Convex Analysis

Set-Valued and Variational Analysis volume 25, pages 731–755 (2017)Cite this article

Abstract

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

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Acknowledgements

The authors are grateful to both anonymous referees for their helpful comments that allowed us to improve the original presentation. The authors are also grateful to Bingwu Wang for helpful discussions on the material presented in this paper.

Research of this author B. S. Mordukhovich was partly supported by the National Science Foundation under grants DMS-1007132 and DMS-1512846, by the Air Force Office of Scientific Research under grant #15RT0462, and by the Ministry of Education and Science of the Russian Federation (Agreement number 02.a03.21.0008 of 24 June 2016).

Research of this author N. M. Nam was partly supported by the National Science Foundation under grant #1411817.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    B. S. Mordukhovich

  2. RUDN University, Moscow, 117198, Russia

    B. S. Mordukhovich

  3. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, 97207, USA

    N. M. Nam, R. B. Rector & T. Tran

Authors
  1. B. S. Mordukhovich
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  2. N. M. Nam
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  3. R. B. Rector
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  4. T. Tran
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Correspondence to B. S. Mordukhovich.

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Dedicated to Michel Théra in honor of his 70th birthday

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Mordukhovich, B.S., Nam, N.M., Rector, R.B. et al. Variational Geometric Approach to Generalized Differential and Conjugate Calculi in Convex Analysis. Set-Valued Var. Anal 25, 731–755 (2017). https://doi.org/10.1007/s11228-017-0426-7

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  • DOI: https://doi.org/10.1007/s11228-017-0426-7

Keywords

  • Convex and variational analysis
  • Fenchel conjugates
  • Normals and subgradients
  • Coderivatives
  • Convex calculus
  • Optimal value functions

Mathematics Subject Classification (2010)

  • 49J52
  • 49J53
  • 90C31