From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization

By Wenqing Chen, Melvyn Sim, Jie Sun, Chung-Piaw Teo. Operational Research, 2010

356 citations recorded by the source corpus.

We review and develop different tractable approximations to individual chance-constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional-value-at-risk (CVaR) measure. We extend the idea to joint chance-constrained problems and provide a new formulation that improves upon the standard approach. Our approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation problem with uncertain demand.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/212c28282d00fe875471ae426319807b3e1b5136

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Citations in the corpus

Distributionally robust joint chance constraints with second-order moment information (2011, methodology): “[9] prove also that their approximation is tighter than the Bonferroni approximation by showing that ZJCC B ( ) ⊆ ⋃ α∈A ZJCC U (α) for all ∈ E .”
Infrastructure Planning for Electric Vehicles with Battery Swapping (2013, methodology): “We develop our models by utilizing recent advances in distributionally-robust optimization [20] [21] [29], a framework for making optimal decisions under limited and/or imprecise information.”
Distributionally Robust Convex Optimization (2014, unknown): “Robust optimization, ambiguous probability distributions, conic optimization.”
Distributionally Robust Optimization: A Review (2019, methodology): “[72] summarize and develop different approximations to the individual chance constraint used in the robust optimization as the consequence of applying different bounds on CVaR.”
Kullback-Leibler divergence constrained distributionally robust optimization (2012, methodology): “Because CCPs are generally nonconvex optimization problems and are often difficult to solve, a convex conservative approximation approach is often used to tackle them (see, e.g., Ben-Tal and Nemirovski 2000, Nemirovski and Shapiro 2006, and Chen et al. 2010).”
Constructing Uncertainty Sets for Robust Linear Optimization (2009, methodology): “Before describing our approach to constructing uncertainty sets, we need some background from risk theory.”
Data-driven chance constrained stochastic program (2015, background): “…constraints (1b), previous research identiﬁes the special cases in which chance constraints are convex (see, e.g., [9,38], and [8]), and, for the general cases in which chance constraints are nonconvex, provides convex conservative approximations and relaxations (see, e.g., [11,32,39], and [1]).”