Subgradient method for minimization of convex functionals and some efficiency bounds
type: Item
instance of: scholarly article
title: Subgradient method for minimization of convex functionals and some efficiency bounds
zbMATH Open document ID: 0688.90044
DOI: 10.1007/BF01095693
author: R. F. Khabibullin
published in: Journal of Soviet Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Consider the problem of minimizing a finite convex functional f on a real Hilbert space E. Let \(\partial f(y)\) be the subdifferential of the functional f at the point \(y\in E\), i.e., \[ \partial f(y)=\{q\in E:\quad f(x)-f(y)\geq <q,x-y>,\quad \forall x\in E\}. \] We propose a solution method for this problem which is conceptually close to the methods of \textit{V. F. Dem'yanov} and \textit{L. V. Vasil'ev} [``Nondifferentiable optimization'' (1985; Zbl 0593.49001) (For a review of the 1981 Russian original see Zbl 0559.49001)] and \textit{C. Lemarechal} [Inform. Processing 74, Proc. IFIP Congr. 74, Stockholm, 552-556 (1974; Zbl 0297.65041)] and estimate its rate of convergence.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 4128661
zbMATH Keywords: finite convex functional
zbMATH Keywords: real Hilbert space
zbMATH Keywords: subdifferential
MaRDI profile type: Publication
cites work: Sufficient conditions for extremum, penalty functions and regularity
full work available at URL: https://doi.org/10.1007/bf01095693
OpenAlex ID: W2083145615
description: scientific article; zbMATH DE number 4128661