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Convergence of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization
Subtitle:Raport Badawczy = Research Report ; RB/48/2005
Creator: Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:11 pages ; 21 cm ; Bibliography p. 10-11
Subject and Keywords:Nonsmooth optimization ; Gradient sampling ; Generalized gradient ; Nonconvex ; Subgradient ; Gradient uogólniony ; Optymalizacja niegładka ; Próbkowanie gradientowe ; Niewypukły
Abstract:The paper deals with the gradient sampling algorithm of Burke, Lewis and Overton for minimizing a locally Lipschitz function f on Rn that is continuously differentiable on an open dense subset. The authors strengthened the existing convergence results for this algorithm, and introduce a slightly revised version for which stronger results are established without requiring compactness of the level sets of f. In particular, it has been shown that with probability 1 the revised algorithm either drives the f -values to -∞, or each of its cluster points is Clarke stationary for f. A simplified variant was also considered in which the differentiability check is skipped and the user can control the number of f -evaluations per iteration.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Creative Commons Attribution BY 4.0 license
Terms of use:Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -
Digitizing institution:Systems Research Institute of the Polish Academy of Sciences
Original in:Library of Systems Research Institute PAS
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