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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| Published in | Mathematical programming Vol. 137; no. 1-2; pp. 167 - 198 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.02.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0025-5610 1436-4646 |
| DOI | 10.1007/s10107-011-0494-7 |
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| 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. |
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| AbstractList | 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. 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.[PUBLICATION ABSTRACT] |
| Author | Zymler, Steve Rustem, Berç Kuhn, Daniel |
| Author_xml | – sequence: 1 givenname: Steve surname: Zymler fullname: Zymler, Steve email: sz02@doc.ic.ac.uk organization: Department of Computing, Imperial College London – sequence: 2 givenname: Daniel surname: Kuhn fullname: Kuhn, Daniel organization: Department of Computing, Imperial College London – sequence: 3 givenname: Berç surname: Rustem fullname: Rustem, Berç organization: Department of Computing, Imperial College London |
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| CODEN | MHPGA4 |
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| SubjectTerms | 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 |
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| Title | Distributionally robust joint chance constraints with second-order moment information |
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