Linear Convergence of Epsilon-Subgradient Descent Methods for a Class of Convex Functions

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4288 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4288 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4288 archive 351 disk0/00/00/49/85 2016-01-15 02:08:05 2021-08-27 17:15:48 2016-01-15 02:08:05 monograph show 2 Robinson S.M. Linear Convergence of Epsilon-Subgradient Descent Methods for a Class of Convex Functions pub iis_met iis_sys prog_opt This paper establishes a linear convergence rate for a class of epsilon-subgradient descent methods for minimizing certain convex functions. Currently prominent methods belonging to this class include the resolvent (proximal point) method and the bundle method in proximal form (considered as a sequence of serious steps). Other methods, such as the recently proposed descent proximal level method, may also fit this framework depending on implementation. The convex functions covered by the analysis are those whose conjugates have subdifferentials that are locally upper Lipschitzian at the origin, a class introduced by Zhang and Treiman. We argue that this class is a natural candidate for study in connection with minimization algorithms. 1996-04 published WP-96-041 WP-96-041 10 public working_paper IIASA, Laxenburg, Austria 11 FALSE info:eu-repo/semantics/book