Probability functions generated by set-valued mappings: a study of first order information
Abstract
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms, giving rise to competitive algorithms in several situations. Probability functions are built up from a random vector belonging to some parameter-dependent subset of the range of a given random vector. In this paper, we investigate first order information of probability functions specified through a convex-valued set-valued application. We provide conditions under which the resulting probability function is indeed locally Lipschitzian as well as subgradient formulae. The resulting formulae are made concrete in a classic optimization setting and put to work in an illustrative example coming from an energy application.
Cite
@article{arxiv.2304.09932,
title = {Probability functions generated by set-valued mappings: a study of first order information},
author = {Wim van Ackooij and Pedro Pérez-Aros and Claudia Soto},
journal= {arXiv preprint arXiv:2304.09932},
year = {2023}
}