Frameworks and Results in Distributionally Robust Optimization

Hamed Rahimian · Sanjay Mehrotra

505 citations0/0 files storedOpen Journal of Mathematical Optimization

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Risk and Portfolio Optimization Optimal Power Flow Distribution Stochastic Gradient Optimization Techniques

Abstract

The concepts of risk aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. The statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and relationships with robust optimization, risk aversion, chance-constrained optimization, and function regularization. Various approaches to model the distributional ambiguity and their calibrations are discussed. The paper also describes the main solution techniques used to the solve the resulting optimization problems.

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References

1999Coherent Measures of Risk 2000Optimization of conditional value-at-risk 2011Introduction to Stochastic Programming 2004The Price of Robustness 1989Maxmin expected utility with non-unique prior 2002Conditional value-at-risk for general loss distributions 2009Robust Optimization 1959Chance-Constrained Programming

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