Superlinear Drift in Consensus-Based Optimization with Condensation Phenomena
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908402240716800 |
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| author | Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia |
| author_facet | Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia |
| contents | Consensus-based optimization (CBO) is a class of metaheuristic algorithms designed for global optimization problems. In the many-particle limit, classical CBO dynamics can be rigorously connected to mean-field equations that ensure convergence toward global minimizers under suitable conditions. In this work, we draw inspiration from recent extensions of the Kaniadakis--Quarati model for indistinguishable bosons to develop a novel CBO method governed by a system of SDEs with superlinear drift and nonconstant diffusion. The resulting mean-field formulation in one dimension exhibits condensation-like phenomena, including finite-time blow-up and loss of $L^2$-regularity. To avoid the curse of dimensionality a marginal based formulation which permits to leverage the one-dimensional results to multiple dimensions is proposed. We support our approach with numerical experiments that highlight both its consistency and potential performance improvements compared to classical CBO methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superlinear Drift in Consensus-Based Optimization with Condensation Phenomena Franceschi, Jonathan Pareschi, Lorenzo Zanella, Mattia Optimization and Control Analysis of PDEs Consensus-based optimization (CBO) is a class of metaheuristic algorithms designed for global optimization problems. In the many-particle limit, classical CBO dynamics can be rigorously connected to mean-field equations that ensure convergence toward global minimizers under suitable conditions. In this work, we draw inspiration from recent extensions of the Kaniadakis--Quarati model for indistinguishable bosons to develop a novel CBO method governed by a system of SDEs with superlinear drift and nonconstant diffusion. The resulting mean-field formulation in one dimension exhibits condensation-like phenomena, including finite-time blow-up and loss of $L^2$-regularity. To avoid the curse of dimensionality a marginal based formulation which permits to leverage the one-dimensional results to multiple dimensions is proposed. We support our approach with numerical experiments that highlight both its consistency and potential performance improvements compared to classical CBO methods. |
| title | Superlinear Drift in Consensus-Based Optimization with Condensation Phenomena |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2506.09001 |