Pessimistic Bilevel Optimization
We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we chara...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/79608 |
| _version_ | 1811076644493852672 |
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| author | Wiesemann, Wolfram Tsoukalas, Angelos Kleniati, Polyxeni-Margarita Rustem, Berc |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Wiesemann, Wolfram Tsoukalas, Angelos Kleniati, Polyxeni-Margarita Rustem, Berc |
| author_sort | Wiesemann, Wolfram |
| collection | MIT |
| description | We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances. |
| first_indexed | 2024-09-23T10:25:22Z |
| format | Article |
| id | mit-1721.1/79608 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:25:22Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/796082022-09-26T17:44:58Z Pessimistic Bilevel Optimization Wiesemann, Wolfram Tsoukalas, Angelos Kleniati, Polyxeni-Margarita Rustem, Berc Massachusetts Institute of Technology. Department of Mechanical Engineering Tsoukalas, Angelos We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances. 2013-07-18T14:26:56Z 2013-07-18T14:26:56Z 2013-02 2012-11 Article http://purl.org/eprint/type/JournalArticle 1052-6234 1095-7189 http://hdl.handle.net/1721.1/79608 Wiesemann, Wolfram, Angelos Tsoukalas, Polyxeni-Margarita Kleniati, and Berç Rustem. “Pessimistic Bilevel Optimization.” SIAM Journal on Optimization 23, no. 1 (February 27, 2013): 353-380. © 2013, Society for Industrial and Applied Mathematics en_US http://dx.doi.org/10.1137/120864015 SIAM Journal on Optimization Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Wiesemann, Wolfram Tsoukalas, Angelos Kleniati, Polyxeni-Margarita Rustem, Berc Pessimistic Bilevel Optimization |
| title | Pessimistic Bilevel Optimization |
| title_full | Pessimistic Bilevel Optimization |
| title_fullStr | Pessimistic Bilevel Optimization |
| title_full_unstemmed | Pessimistic Bilevel Optimization |
| title_short | Pessimistic Bilevel Optimization |
| title_sort | pessimistic bilevel optimization |
| url | http://hdl.handle.net/1721.1/79608 |
| work_keys_str_mv | AT wiesemannwolfram pessimisticbileveloptimization AT tsoukalasangelos pessimisticbileveloptimization AT kleniatipolyxenimargarita pessimisticbileveloptimization AT rustemberc pessimisticbileveloptimization |