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Extension of Subgradient Techniques for Nonsmooth Optimization in Banach Spaces
Authors:Ya. I. Alber and A. N. Iusem
Affiliation:(1) Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel;(2) Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil
Abstract:In this paper we continue the study of the subgradient method for nonsmooth convex constrained minimization problems in a uniformly convex and uniformly smooth Banach space. We consider the case when the stepsizes satisfy sumk=1infinagrk=infin, limthinspkrarrinfinagrk=0.
Keywords:subgradient method  nonsmooth convex functional  subgradient  duality mapping  generalized projection  J-Lipschitz continuous functional  weak convergence  estimates of convergence rate
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