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


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.
Number of pages6
ISBN (Electronic)9798350301243
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


Conference62nd IEEE Conference on Decision and Control, CDC 2023

All Science Journal Classification (ASJC) codes

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

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