2023/04/19 by Wim van Ackooij, van Ackooij, Wim, Pedro Pérez-Aros +3
Decision Sciences · Engineering · Mathematics · #90C15 #FOS: Mathematics #Fuzzy Systems and Optimization #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Water resources management and optimization
paper · pdf · doi:10.48550/arxiv.2304.09932
openalex publication_date 2023/04/19 · openalex created_date 2023/04/24 · openalex updated_date 2026/07/28
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.