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Generalized Sequential Differential Calculus for Expected-Integral Functionals

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Abstract

Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the second one an integrable function. The main goal of this paper is to establish sequential versions of Leibniz’s rule for regular subgradients by employing and developing appropriate tools of variational analysis.

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Acknowledgments

The authors are grateful to anonymous referees for their helpful remarks that allowed us to improve the original presentation.

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Authors and Affiliations

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

    Boris S. Mordukhovich

  2. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    Pedro Pérez-Aros

Authors
  1. Boris S. Mordukhovich
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  2. Pedro Pérez-Aros
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Correspondence to Boris S. Mordukhovich.

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Dedicated to Terry Rockafellar, in high esteem

Research of the first author was partially supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research under grant #15RT04, and by the Australian Research Council under Discovery Project DP-190100555. Research of the second author was partially supported by grants: Fondecyt Regular 1190110 and Fondecyt Regular 1200283.

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Mordukhovich, B.S., Pérez-Aros, P. Generalized Sequential Differential Calculus for Expected-Integral Functionals. Set-Valued Var. Anal 29, 621–644 (2021). https://doi.org/10.1007/s11228-021-00590-4

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  • DOI: https://doi.org/10.1007/s11228-021-00590-4

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