COSMO: A conic operator splitting method for convex conic problems
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 l...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2021
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| _version_ | 1797091973456199680 |
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| author | Garstka, M Cannon, M Goulart, P |
| author_facet | Garstka, M Cannon, M Goulart, P |
| author_sort | Garstka, M |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T03:40:00Z |
| format | Journal article |
| id | oxford-uuid:bd90358e-1778-4833-b848-4bcd86b4229f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:40:00Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:bd90358e-1778-4833-b848-4bcd86b4229f2022-03-27T05:32:43ZCOSMO: A conic operator splitting method for convex conic problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bd90358e-1778-4833-b848-4bcd86b4229fEnglishSymplectic ElementsSpringer2021Garstka, MCannon, MGoulart, PThis 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. |
| spellingShingle | Garstka, M Cannon, M Goulart, P COSMO: A conic operator splitting method for convex conic problems |
| title | COSMO: A conic operator splitting method for convex conic problems |
| title_full | COSMO: A conic operator splitting method for convex conic problems |
| title_fullStr | COSMO: A conic operator splitting method for convex conic problems |
| title_full_unstemmed | COSMO: A conic operator splitting method for convex conic problems |
| title_short | COSMO: A conic operator splitting method for convex conic problems |
| title_sort | cosmo a conic operator splitting method for convex conic problems |
| work_keys_str_mv | AT garstkam cosmoaconicoperatorsplittingmethodforconvexconicproblems AT cannonm cosmoaconicoperatorsplittingmethodforconvexconicproblems AT goulartp cosmoaconicoperatorsplittingmethodforconvexconicproblems |