Distributionally robust joint chance constraints with second-order moment information

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...

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Vydané v:Mathematical programming Ročník 137; číslo 1-2; s. 167 - 198
Hlavní autori: Zymler, Steve, Kuhn, Daniel, Rustem, Berç
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer-Verlag 01.02.2013
Springer Nature B.V
Predmet:
Analysis
Approximation
Benchmarking
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Dynamic tests
Full Length Paper
Inequality
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Probability
Probability distribution
Programming
Semidefinite programming
Studies
Theoretical
Tightness
90C22
90C15
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-011-0494-7