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@ARTICLE{Bungert:640480,
      author       = {Bungert, Leon and Hoffmann, Franca and Kim, Dohyeon and
                      Roith, Tim},
      title        = {{M}irror{CBO}: {A} consensus-based optimization method in
                      the spirit of mirror descent},
      reportid     = {PUBDB-2025-04802, arXiv:2501.12189},
      year         = {2025},
      note         = {66 pages, 18 figures, 19 tables},
      abstract     = {In this work we propose MirrorCBO, a consensus-based
                      optimization (CBO) method which generalizes standard CBO in
                      the same way that mirror descent generalizes gradient
                      descent. For this we apply the CBO methodology to a swarm of
                      dual particles and retain the primal particle positions by
                      applying the inverse of the mirror map, which we parametrize
                      as the subdifferential of a strongly convex function $ϕ$.
                      In this way, we combine the advantages of a derivative-free
                      non-convex optimization algorithm with those of mirror
                      descent. As a special case, the method extends CBO to
                      optimization problems with convex constraints. Assuming
                      bounds on the Bregman distance associated to $ϕ$, we
                      provide asymptotic convergence results for MirrorCBO with
                      explicit exponential rate. Another key contribution is an
                      exploratory numerical study of this new algorithm across
                      different application settings, focusing on (i)
                      sparsity-inducing optimization, and (ii) constrained
                      optimization, demonstrating the competitive performance of
                      MirrorCBO. We observe empirically that the method can also
                      be used for optimization on (non-convex) submanifolds of
                      Euclidean space, can be adapted to mirrored versions of
                      other recent CBO variants, and that it inherits from mirror
                      descent the capability to select desirable minimizers, like
                      sparse ones. We also include an overview of recent CBO
                      approaches for constrained optimization and compare their
                      performance to MirrorCBO.},
      cin          = {FS-CI},
      cid          = {I:(DE-H253)FS-CI-20230420},
      pnm          = {623 - Data Management and Analysis (POF4-623) / DFG project
                      G:(GEPRIS)544579844 - GeoMAR: Geometrische Methoden für
                      Adversarial Robustness (544579844)},
      pid          = {G:(DE-HGF)POF4-623 / G:(GEPRIS)544579844},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2501.12189},
      howpublished = {arXiv:2501.12189},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2501.12189;\%\%$},
      url          = {https://bib-pubdb1.desy.de/record/640480},
}