Robust convex optimization: A new perspective that unifies and extends
Abstract Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them i...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2022
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| Online Access: | https://hdl.handle.net/1721.1/145481 |
| _version_ | 1811095819072307200 |
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| author | Bertsimas, Dimitris Hertog, Dick d. Pauphilet, Jean Zhen, Jianzhe |
| author2 | Sloan School of Management |
| author_facet | Sloan School of Management Bertsimas, Dimitris Hertog, Dick d. Pauphilet, Jean Zhen, Jianzhe |
| author_sort | Bertsimas, Dimitris |
| collection | MIT |
| description | Abstract
Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the ones proposed in the literature, or obtaining solutions for classes of problems unaddressed by previous approaches. Our solution is based on an extension of the Reformulation-Linearization-Technique, and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations which can be used to obtain both upper- and lower- bounds for the optimal objective value. We illustrate the numerical benefit of our approach on a robust control and robust geometric optimization example. |
| first_indexed | 2024-09-23T16:29:17Z |
| format | Article |
| id | mit-1721.1/145481 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:29:17Z |
| publishDate | 2022 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1454812022-09-29T19:59:53Z Robust convex optimization: A new perspective that unifies and extends Bertsimas, Dimitris Hertog, Dick d. Pauphilet, Jean Zhen, Jianzhe Sloan School of Management Abstract Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the ones proposed in the literature, or obtaining solutions for classes of problems unaddressed by previous approaches. Our solution is based on an extension of the Reformulation-Linearization-Technique, and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations which can be used to obtain both upper- and lower- bounds for the optimal objective value. We illustrate the numerical benefit of our approach on a robust control and robust geometric optimization example. 2022-09-19T13:56:35Z 2022-09-19T13:56:35Z 2022-09-12 2022-09-18T03:13:08Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145481 Bertsimas, Dimitris, Hertog, Dick d., Pauphilet, Jean and Zhen, Jianzhe. 2022. "Robust convex optimization: A new perspective that unifies and extends." PUBLISHER_CC en https://doi.org/10.1007/s10107-022-01881-w Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Bertsimas, Dimitris Hertog, Dick d. Pauphilet, Jean Zhen, Jianzhe Robust convex optimization: A new perspective that unifies and extends |
| title | Robust convex optimization: A new perspective that unifies and extends |
| title_full | Robust convex optimization: A new perspective that unifies and extends |
| title_fullStr | Robust convex optimization: A new perspective that unifies and extends |
| title_full_unstemmed | Robust convex optimization: A new perspective that unifies and extends |
| title_short | Robust convex optimization: A new perspective that unifies and extends |
| title_sort | robust convex optimization a new perspective that unifies and extends |
| url | https://hdl.handle.net/1721.1/145481 |
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