Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints
We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman inversion (EKI). Unlike other approaches in the literature, the m...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Book section |
| Language: | English |
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World Scientific Publishing
2023
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| _version_ | 1826312063898615808 |
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| author | Carrillo, JA Totzeck, C Vaes, U |
| author2 | Bao, W |
| author_facet | Bao, W Carrillo, JA Totzeck, C Vaes, U |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman inversion (EKI). Unlike other approaches in the literature, the method we propose does not constrain the dynamics to the feasible region of the state space at all times; the particles evolve in the full space, but are attracted towards the feasible set by means of a penalization term added to the objective function and, in the case of CBO, an additional relaxation drift. We study the properties of the method through the associated mean-field Fokker–Planck equation and demonstrate its performance in numerical experiments on several test problems. |
| first_indexed | 2024-03-07T08:22:01Z |
| format | Book section |
| id | oxford-uuid:b1816e51-3a62-4b05-9cef-b6a09ab6d14d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:22:01Z |
| publishDate | 2023 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:b1816e51-3a62-4b05-9cef-b6a09ab6d14d2024-02-05T09:22:02ZConsensus-based optimization and ensemble Kalman inversion for global optimization problems with constraintsBook sectionhttp://purl.org/coar/resource_type/c_1843uuid:b1816e51-3a62-4b05-9cef-b6a09ab6d14dEnglishSymplectic ElementsWorld Scientific Publishing2023Carrillo, JATotzeck, CVaes, UBao, WMarkowich, PAPerthame, BTadmor, EWe introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman inversion (EKI). Unlike other approaches in the literature, the method we propose does not constrain the dynamics to the feasible region of the state space at all times; the particles evolve in the full space, but are attracted towards the feasible set by means of a penalization term added to the objective function and, in the case of CBO, an additional relaxation drift. We study the properties of the method through the associated mean-field Fokker–Planck equation and demonstrate its performance in numerical experiments on several test problems. |
| spellingShingle | Carrillo, JA Totzeck, C Vaes, U Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title | Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title_full | Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title_fullStr | Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title_full_unstemmed | Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title_short | Consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints |
| title_sort | consensus based optimization and ensemble kalman inversion for global optimization problems with constraints |
| work_keys_str_mv | AT carrilloja consensusbasedoptimizationandensemblekalmaninversionforglobaloptimizationproblemswithconstraints AT totzeckc consensusbasedoptimizationandensemblekalmaninversionforglobaloptimizationproblemswithconstraints AT vaesu consensusbasedoptimizationandensemblekalmaninversionforglobaloptimizationproblemswithconstraints |