Journal article
COSMO: A conic operator splitting method for convex conic problems
- Abstract:
- This paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package for convex optimisation problems with quadratic objective function and conic constraints. At each step, the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark problems show the effectiveness of our approach. Our Julia implementation is open source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 979.0KB, Terms of use)
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- Publisher copy:
- 10.1007/s10957-021-01896-x
Authors
- Publisher:
- Springer
- Journal:
- Journal of Optimization Theory and Applications More from this journal
- Volume:
- 190
- Issue:
- 3
- Pages:
- 779-810
- Publication date:
- 2021-08-29
- Acceptance date:
- 2021-06-16
- DOI:
- EISSN:
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1573-2878
- ISSN:
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0022-3239
- Language:
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English
- Keywords:
- Pubs id:
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1207653
- Local pid:
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pubs:1207653
- Deposit date:
-
2021-11-09
Terms of use
- Copyright holder:
- Crown Copyright.
- Copyright date:
- 2021
- Rights statement:
- © Crown 2021. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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