A variant of the constrained gradient method
type: Item
instance of: scholarly article
title: A variant of the constrained gradient method
zbMATH Open document ID: 0696.90047
DOI: 10.1007/BF01098003
author: E. V. Lyamin
author: Igor Yaroslavich Zabotin
published in: Journal of Soviet Mathematics
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/198159
review text: The authors consider the method of conditional gradients applied to a mathematical program of minimizing a convex differentiable functional \(\phi\) (x) over a convex set \(D\subset {\mathbb{R}}^ n\). The corresponding iterative algorithm can be described as follows. Let \(x_ k\) be a current guess. Find \(y_ k\in S_ k=\{x_ k+S\}\cap D\) such that: \[ (1)\quad (y_ k-x_ k)^ T\nabla \phi (x_ k)\leq t_ k\quad \min \{(y-x_ k)^ T\nabla \phi (x_ k):\quad y\in S_ k\}, \] where S is a convex compact neighborhood of zero and \(t_ k\in (0,1]\). Then put \(x_{k+1}=x_ k+\lambda_ k(y_ k-x_ k)\) for some \(\lambda_ k\in [0,1].\) Some simple procedures for choosing parameters \(t_ k\) and \(\lambda_ k\), ensuring convergence of the algorithm, are given. A method for solving problem (1), when the sets D and S are defined by inequality constraints, is proposed.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C52
zbMATH DE Number: 4141796
zbMATH Keywords: conditional gradients
zbMATH Keywords: convex differentiable functional
zbMATH Keywords: convergence
zbMATH Keywords: inequality constraints
MaRDI profile type: Publication
cites work: Iterative regularization of one version of the conditional-gradient method
description: scientific article; zbMATH DE number 4141796