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arXiv · 2101.06711

Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings

Boris S. Mordukhovich·Pedro Pérez-Aros
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Abstract

This paper is devoted to the study of the expected-integral multifunctions given in the form \begin{equation*} \operatorname{E}_Φ(x):=\int_TΦ_t(x)dμ, \end{equation*} where $Φ\colon T\times\mathbb{R}^n \rightrightarrows \mathbb{R}^m$ is a set-valued mapping on a measure space $(T,\mathcal{A},μ)$. Such multifunctions appear in applications to stochastic programming, which require developing efficient calculus rules of generalized differentiation. Major calculus rules are developed in this paper for coderivatives of multifunctions $\operatorname{E}_Φ$ and second-order subdifferentials of the corresponding expected-integral functionals with applications to constraint systems arising in stochastic programming. The paper is self-contained with presenting in the preliminaries some needed results on sequential first-order subdifferential calculus of expected-integral functionals taken from the first paper of this series.

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Boris S. Mordukhovich, Pedro Pérez-Aros. 2021-06-18. Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings. https://arxiv.org/abs/2101.06711

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