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Codifferentials and Quasidifferentials of the Expectation of Nonsmooth Random Integrands and Two-Stage Stochastic Programming

In: High-Dimensional Optimization and Probability

Author

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  • M. V. Dolgopolik

    (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences)

Abstract

This work is devoted to an analysis of exact penalty functions and optimality conditions for nonsmooth two-stage stochastic programming problems. To this end, we first study the co/quasidifferentiability of the expectation of nonsmooth random integrands and obtain explicit formulae for its co and quasidifferential under some natural assumptions on the integrand. Then, we analyse exact penalty functions for a variational reformulation of two-stage stochastic programming problems and obtain sufficient conditions for the global exactness of these functions with two different penalty terms. In the end of the chapter, we combine our results on the co/quasidifferentiability of the expectation of nonsmooth random integrands and exact penalty functions to derive optimality conditions for nonsmooth two-stage stochastic programming problems in terms of codifferentials.

Suggested Citation

  • M. V. Dolgopolik, 2022. "Codifferentials and Quasidifferentials of the Expectation of Nonsmooth Random Integrands and Two-Stage Stochastic Programming," Springer Optimization and Its Applications, in: Ashkan Nikeghbali & Panos M. Pardalos & Andrei M. Raigorodskii & Michael Th. Rassias (ed.), High-Dimensional Optimization and Probability, pages 185-218, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-00832-0_5
    DOI: 10.1007/978-3-031-00832-0_5
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