A distributionally robust perspective on uncertainty quantification and chance constrained programming
The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be mo...
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| Vydáno v: | Mathematical programming Ročník 151; číslo 1; s. 35 - 62 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2015
Springer Nature B.V |
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| ISSN: | 0025-5610, 1436-4646 |
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| Abstract | The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones. |
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| AbstractList | Issue Title: Special Issue: International Symposium on Mathematical Programming, Pittsburgh, July 2015 The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones. The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones. |
| Author | Wiesemann, Wolfram Hanasusanto, Grani A. Roitch, Vladimir Kuhn, Daniel |
| Author_xml | – sequence: 1 givenname: Grani A. surname: Hanasusanto fullname: Hanasusanto, Grani A. organization: Department of Computing, Imperial College London – sequence: 2 givenname: Vladimir surname: Roitch fullname: Roitch, Vladimir organization: Department of Computing, Imperial College London – sequence: 3 givenname: Daniel surname: Kuhn fullname: Kuhn, Daniel email: daniel.kuhn@epfl.ch organization: Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne – sequence: 4 givenname: Wolfram surname: Wiesemann fullname: Wiesemann, Wolfram organization: Imperial College Business School, Imperial College London |
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