Daniilidis, A., & Salas, D. (2024). Steepest Geometric Descent for Regularized Quasiconvex Functions. Set-Valued and Variational Analysis, 32(3), Article 28. https://doi.org/10.1007/s11228-024-00731-5
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Set-Valued and Variational Analysis
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ISSN:
1877-0533
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Date (published):
Aug-2024
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Publisher:
SPRINGER
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Peer reviewed:
Yes
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Keywords:
Max-convolution; Quasiconvex functions; Steepest descent curves; Sweeping process
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Abstract:
We establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process flow induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in a more general setting.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
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Project (external):
FONDECYT (ANID, Chile) BASAL fund (Centers of excellence, ANID, Chile).
