Convex Chance-Constrained Programs with Wasserstein Ambiguity

Haoming Shen () and Ruiwei Jiang ()
Additional contact information
Haoming Shen: Department of Industrial Engineering, University of Arkansas, Fayetteville, Arkansas 72703
Ruiwei Jiang: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109

Operations Research, 2025, vol. 73, issue 4, 2264-2280

Abstract: Chance constraints yield nonconvex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, existing studies showed that the distributionally robust (pessimistic) chance constraint admits a mixed-integer conic representation. This paper identifies sufficient conditions that lead to convex feasible regions of chance constraints with Wasserstein ambiguity. First, when uncertainty arises from the right-hand side of a pessimistic joint chance constraint, we show that the ensuing feasible region is convex if the Wasserstein ball is centered around a log-concave distribution (or, more generally, an α -concave distribution with α ≥ − 1 ). In addition, we propose a block coordinate ascent algorithm and prove its convergence to global optimum, as well as the rate of convergence. Second, when uncertainty arises from the left-hand side of a pessimistic two-sided chance constraint, we show the convexity if the Wasserstein ball is centered around an elliptical and star unimodal distribution. In addition, we propose a family of second-order conic inner approximations, and we bound their approximation error and prove their asymptotic exactness. Furthermore, we extend the convexity results to optimistic chance constraints.

Keywords: Optimization; chance constraints; convexity; Wasserstein ambiguity; distributionally robust optimization; distributionally optimistic optimization (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/opre.2021.0709 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:4:p:2264-2280

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().