Global Resolution of Chance-Constrained Optimization Problems: Minkowski Functionals and Monotone Inclusions

Peixuan Zhang, Uday V. Shanbhag, Constantino M. Lagoa, Ibrahim E. Bardakci

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Chance-constrained optimization problems, an important subclass of stochastic optimization problems, are often complicated by nonsmoothness, and nonconvexity. Thus far, non-asymptotic rates and complexity guarantees for computing an ϵ-global minimizer remain open questions. We consider a subclass of problems in which the probability is defined as P ζ| ζ∈ K(x), where K is a set defined as K(x) = ζ∈ K| c(x, ζ)≤ 1}, c(x, •) is a positively homogeneous function for any x ∈ X, and K is a nonempty and convex set, symmetric about the origin. We make two contributions in this context. (i) First, when ζ admits a log-concave density on K, the probability function is equivalent to an expectation of a nonsmooth Clarke-regular integrand, allowing for the chance-constrained problem to be restated as a convex program. Under a suitable regularity condition, the necessary and sufficient conditions of this problem are given by a monotone inclusion with a compositional expectation-valued operator. (ii) Second, when ζ admits a uniform density, we present a variance-reduced proximal scheme and provide amongst the first rate and complexity guarantees for resolving chance-constrained optimization problems.

Original languageEnglish (US)
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6301-6306
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: Dec 13 2023Dec 15 2023

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period12/13/2312/15/23

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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