Risk minimization, regret minimization and progressive hedging algorithms
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship open...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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SPRINGER HEIDELBERG
2020
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/91434 |
| _version_ | 1848765519558082560 |
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| author | Sun, Jie Yang, X. Yao, Q. Zhang, M. |
| author_facet | Sun, Jie Yang, X. Yao, Q. Zhang, M. |
| author_sort | Sun, Jie |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms. |
| first_indexed | 2025-11-14T11:36:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-91434 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:33Z |
| publishDate | 2020 |
| publisher | SPRINGER HEIDELBERG |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914342024-04-11T02:56:54Z Risk minimization, regret minimization and progressive hedging algorithms Sun, Jie Yang, X. Yao, Q. Zhang, M. Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Progressive hedging algorithm Regret minimization Risk measures Stochastic optimization This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms. 2020 Journal Article http://hdl.handle.net/20.500.11937/91434 10.1007/s10107-020-01471-8 English http://purl.org/au-research/grants/arc/DP160102819 SPRINGER HEIDELBERG fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Progressive hedging algorithm Regret minimization Risk measures Stochastic optimization Sun, Jie Yang, X. Yao, Q. Zhang, M. Risk minimization, regret minimization and progressive hedging algorithms |
| title | Risk minimization, regret minimization and progressive hedging algorithms |
| title_full | Risk minimization, regret minimization and progressive hedging algorithms |
| title_fullStr | Risk minimization, regret minimization and progressive hedging algorithms |
| title_full_unstemmed | Risk minimization, regret minimization and progressive hedging algorithms |
| title_short | Risk minimization, regret minimization and progressive hedging algorithms |
| title_sort | risk minimization, regret minimization and progressive hedging algorithms |
| topic | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics Progressive hedging algorithm Regret minimization Risk measures Stochastic optimization |
| url | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/91434 |