Convex Chance-Constrained Programs with Wasserstein Ambiguity

• 成果类型: Article
• 署名作者: Shen, Haoming; Jiang, Ruiwei
• 署名单位: University of Arkansas System; University of Arkansas Fayetteville; University of Michigan System; University of Michigan
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.0709
• 发表日期: 2025
• 页码: 2264-2280
• 关键词: Optimization; approximation; CONVERGENCE; MODEL

摘要

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 alpha-concave distribution with alpha >=-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.