Computing Conjugate Barrier Information for Nonsymmetric Cones
Abstract The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of w...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/144398 |
| _version_ | 1826217565801676800 |
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| author | Kapelevich, Lea Andersen, Erling D. Vielma, Juan P. |
| author2 | Massachusetts Institute of Technology. Operations Research Center |
| author_facet | Massachusetts Institute of Technology. Operations Research Center Kapelevich, Lea Andersen, Erling D. Vielma, Juan P. |
| author_sort | Kapelevich, Lea |
| collection | MIT |
| description | Abstract
The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier. |
| first_indexed | 2024-09-23T17:05:42Z |
| format | Article |
| id | mit-1721.1/144398 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:05:42Z |
| publishDate | 2022 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1443982023-01-09T21:18:22Z Computing Conjugate Barrier Information for Nonsymmetric Cones Kapelevich, Lea Andersen, Erling D. Vielma, Juan P. Massachusetts Institute of Technology. Operations Research Center Sloan School of Management Abstract The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier. 2022-08-22T12:59:31Z 2022-08-22T12:59:31Z 2022-08-20 2022-08-21T03:10:48Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/144398 Kapelevich, Lea, Andersen, Erling D. and Vielma, Juan P. 2022. "Computing Conjugate Barrier Information for Nonsymmetric Cones." PUBLISHER_CC en https://doi.org/10.1007/s10957-022-02076-1 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer US Springer US |
| spellingShingle | Kapelevich, Lea Andersen, Erling D. Vielma, Juan P. Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title | Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title_full | Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title_fullStr | Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title_full_unstemmed | Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title_short | Computing Conjugate Barrier Information for Nonsymmetric Cones |
| title_sort | computing conjugate barrier information for nonsymmetric cones |
| url | https://hdl.handle.net/1721.1/144398 |
| work_keys_str_mv | AT kapelevichlea computingconjugatebarrierinformationfornonsymmetriccones AT andersenerlingd computingconjugatebarrierinformationfornonsymmetriccones AT vielmajuanp computingconjugatebarrierinformationfornonsymmetriccones |