TY - GEN

T1 - Global Resolution of Chance-Constrained Optimization Problems

T2 - 62nd IEEE Conference on Decision and Control, CDC 2023

AU - Zhang, Peixuan

AU - Shanbhag, Uday V.

AU - Lagoa, Constantino M.

AU - Bardakci, Ibrahim E.

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.1109/CDC49753.2023.10383862

DO - 10.1109/CDC49753.2023.10383862

M3 - Conference contribution

AN - SCOPUS:85184809910

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 6301

EP - 6306

BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 13 December 2023 through 15 December 2023

ER -