Constructing Uncertainty Sets for Robust Linear Optimization

By Dimitris J. Bertsimas, David B. Brown. Operational Research, 2009

396 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/252d5d83b565b9351cdc36b248cde6730dfeaaaf

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics (2017, background): “sk metrics fulﬁlling these axioms corresponds precisely to the class of distortion risk metrics, which form a subset of coherent risk metrics and have previously been studied in the ﬁnance literature [32, 16, 12, 5]. As discussed previously, the most commonly used risk metrics in robotics are the ex”
Offering Strategy Via Robust Optimization (2011, background): “Managing risk through robust optimization and through stochastic programming incorporatingrisk measures (e.g.,the conditionalvalueatrisk,CVaR)isequivalentunder certainassumptions as shown by Bertsimas et al., [ 25 ].”
ON NONSMOOTH OPTIMALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS (2014, background): “Robust optimization, which has emerged as a powerful deterministic approach for studying optimization problems under uncertainty [3, 5, 6, 7], associates with the uncertain program (UP) its robust counterpart [2, 4, 16], (RP) inf{f(x) | gi(x, vi) ≤ 0, ∀vi ∈ Vi, i = 1, .”
Distributionally Robust Convex Optimization (2014, neutral): “Robust optimization, ambiguous probability distributions, conic optimization.”
Recent advances in robust optimization: An overview (2014, background): “Bertsimas and Brown (2009) describe how to connect uncertainty sets in robust linear optimization to coherent risk measures, an example of which is CVaR.”
A practical guide to robust optimization (2015, background): “Bertsimas and Brown (2009) show how to construct uncertainty sets based on coherent risk measures that model the preferences of the decision maker, and on past observations of the uncertain data.”
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities (2013, positive): “Bertsimas and Brown [7] interpret robust optimization in terms of coherent risk measures.”
Data-driven robust optimization (2013, background): “Remark 4 The sets Uχ2 , U strongly resemble the uncertainty set for CVaR P̂ in [11].”
From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization (2010, methodology): “Recent works of Bertsimas and Brown [8] and Natarajan et al. [24] have uncovered the relation between financial risk measures and uncertainty sets in robust optimization.”
Theory and Applications of Robust Optimization (2010, result): “Bertsimas and Brown [23] examine the question from the opposite perspective: namely, with risk preferences speciﬁed by a coherent risk measure, they examine the implications for uncertainty set structure in robust linear optimization problems.”