Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme
We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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AMER INST MATHEMATICAL SCIENCES-AIMS
2021
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/90790 |
| _version_ | 1848765429047099392 |
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| author | Yu, H. Sun, Jie |
| author_facet | Yu, H. Sun, Jie |
| author_sort | Yu, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a Finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method. |
| first_indexed | 2025-11-14T11:35:06Z |
| format | Journal Article |
| id | curtin-20.500.11937-90790 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:35:06Z |
| publishDate | 2021 |
| publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-907902023-05-11T01:50:17Z Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme Yu, H. Sun, Jie Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Stochastic optimization distributionally robust convex risk measure subgradient method two-stage optimization problem LINEAR OPTIMIZATION PROGRAMS MODELS We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a Finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method. 2021 Journal Article http://hdl.handle.net/20.500.11937/90790 10.3934/jimo.2019100 English http://purl.org/au-research/grants/arc/DP160102819 AMER INST MATHEMATICAL SCIENCES-AIMS restricted |
| spellingShingle | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Stochastic optimization distributionally robust convex risk measure subgradient method two-stage optimization problem LINEAR OPTIMIZATION PROGRAMS MODELS Yu, H. Sun, Jie Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title | Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title_full | Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title_fullStr | Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title_full_unstemmed | Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title_short | Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme |
| title_sort | robust stochastic optimization with convex risk measures: a discretized subgradient scheme |
| topic | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Stochastic optimization distributionally robust convex risk measure subgradient method two-stage optimization problem LINEAR OPTIMIZATION PROGRAMS MODELS |
| url | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/90790 |