Journal ArticleDOI
Distributionally robust joint chance constraints with second-order moment information
TLDR
It is proved that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and it is demonstrated that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions.Abstract:
We develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and we demonstrate that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions. Next, we study the Worst-Case CVaR approximation for joint chance constraints. This approximation affords intuitive dual interpretations and is provably tighter than two popular benchmark approximations. The tightness depends on a set of scaling parameters, which can be tuned via a sequential convex optimization algorithm. We show that the approximation becomes essentially exact when the scaling parameters are chosen optimally and that the Worst-Case CVaR can be evaluated efficiently if the scaling parameters are kept constant. We evaluate our joint chance constraint approximation in the context of a dynamic water reservoir control problem and numerically demonstrate its superiority over the two benchmark approximations.read more
Citations
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Distributionally Robust Convex Optimization
TL;DR: A unifying framework for modeling and solving distributionally robust optimization problems and introduces standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold.
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Recent advances in robust optimization: An overview☆
TL;DR: An overview of developments in robust optimization since 2007 is provided to give a representative picture of the research topics most explored in recent years, highlight common themes in the investigations of independent research teams and highlight the contributions of rising as well as established researchers both to the theory of robust optimization and its practice.
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Distributionally Robust Stochastic Optimization with Wasserstein Distance
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TL;DR: The paper argues that the set of distributions chosen should be chosen to be appropriate for the application at hand, and that some of the choices that have been popular until recently are, for many applications, not good choices.
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Data-driven chance constrained stochastic program
Ruiwei Jiang,Yongpei Guan +1 more
TL;DR: This paper derives an equivalent reformulation for DCC and shows that it is equivalent to a classical chance constraint with a perturbed risk level, and analyzes the relationship between the conservatism of D CC and the size of historical data, which can help indicate the value of data.
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Distributionally Robust Optimization: A Review
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TL;DR: Main concepts and contributions to DRO are surveyed, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization are surveyed.
References
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Journal ArticleDOI
On Distributionally Robust Chance-Constrained Linear Programs
TL;DR: It is shown that, for a wide class of probability distributions on the data, the probability constraints can be converted explicitly into convex second-order cone constraints; hence the probability-constrained linear program can be solved exactly with great efficiency.
Journal ArticleDOI
Chance Constrained Programming with Joint Constraints
Bruce L. Miller,Harvey M. Wagner +1 more
TL;DR: In this article, the authors consider the mathematical properties of chance constrained programming problems where the restriction is on the joint probability of a multivariate random event and explore whether the resultant problem meets the concavity assumption.
Journal ArticleDOI
A Robust Optimization Perspective on Stochastic Programming
Xin Chen,Melvyn Sim,Peng Sun +2 more
TL;DR: An approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations is introduced, which converts the original model into a second-order cone program, which is computationally tractable both in theory and in practice.
Proceedings ArticleDOI
On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback
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On duality theory of conic linear problems
TL;DR: In this article, duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems, is discussed, where the questions of no duality gap and existence of optimal solutions are related to properties of the corresponding optimal value function.
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