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@ARTICLE{Bungert:607321,
      author       = {Bungert, Leon and Roith, Tim and Wacker, Philipp},
      title        = {{P}olarized consensus-based dynamics for optimization and
                      sampling},
      journal      = {Mathematical programming},
      volume       = {21},
      issn         = {0025-5610},
      address      = {Heidelberg},
      publisher    = {Springer},
      reportid     = {PUBDB-2024-01832},
      pages        = {125 - 155},
      year         = {2024},
      note         = {L:MB},
      abstract     = {In this paper we propose polarized consensus-based dynamics
                      in order to make consensus-based optimization (CBO) and
                      sampling (CBS) applicable for objective functions with
                      several global minima or distributions with many modes,
                      respectively. For this, we ``polarize'' the dynamics with a
                      localizing kernel and the resulting model can be viewed as a
                      bounded confidence model for opinion formation in the
                      presence of common objective. Instead of being attracted to
                      a common weighted mean as in the original consensus-based
                      methods, which prevents the detection of more than one
                      minimum or mode, in our method every particle is attracted
                      to a weighted mean which gives more weight to nearby
                      particles. We prove that in the mean-field regime the
                      polarized CBS dynamics are unbiased for Gaussian targets. We
                      also prove that in the zero temperature limit and for
                      sufficiently well-behaved strongly convex objectives the
                      solution of the Fokker--Planck equation converges in the
                      Wasserstein-2 distance to a Dirac measure at the minimizer.
                      Finally, we propose a computationally more efficient
                      generalization which works with a predefined number of
                      clusters and improves upon our polarized baseline method for
                      high-dimensional optimization.},
      cin          = {FS-CI},
      ddc          = {510},
      cid          = {I:(DE-H253)FS-CI-20230420},
      pnm          = {623 - Data Management and Analysis (POF4-623) / DFG project
                      G:(GEPRIS)390685689 - EXC 2046: MATH+: Berlin Mathematics
                      Research Center (390685689) / 05M20WEA - Verbundprojekt
                      05M2020 - DELETO: Maschinelles Lernen bei korrelativer MR
                      und Hochdurchsatz-NanoCT. Teilvorhaben 3: Gelernte
                      Regularisierungsmethoden und lernbasierte Verfahren für
                      korrelatives MR. (BMBF-05M20WEA) / NoMADS - Nonlocal Methods
                      for Arbitrary Data Sources (777826)},
      pid          = {G:(DE-HGF)POF4-623 / G:(GEPRIS)390685689 /
                      G:(DE-Ds200)BMBF-05M20WEA / G:(EU-Grant)777826},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2211.05238},
      howpublished = {arXiv:2211.05238},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2211.05238;\%\%$},
      UT           = {WOS:001236090900001},
      doi          = {10.1007/s10107-024-02095-y},
      url          = {https://bib-pubdb1.desy.de/record/607321},
}