A GENERALIZED SUBGRADIENT METHOD WITH RELAXATION STEP

Authors
Citation
U. Brannlund, A GENERALIZED SUBGRADIENT METHOD WITH RELAXATION STEP, Mathematical programming, 71(2), 1995, pp. 207-219
Citations number
16
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science",Mathematics,"Computer Science Software Graphycs Programming
Journal title
ISSN journal
0025-5610
Volume
71
Issue
2
Year of publication
1995
Pages
207 - 219
Database
ISI
SICI code
0025-5610(1995)71:2<207:AGSMWR>2.0.ZU;2-7
Abstract
We study conditions for convergence of a generalized subgradient algor ithm in which a relaxation step is taken in a direction, which is a co nvex combination of possibly all previously generated subgradients. A simple condition for convergence is given and conditions that guarante e a linear convergence rate are also presented. We show that choosing the steplength parameter and convex combination of subgradients in a c ertain sense optimally is equivalent to solving a minimum norm quadrat ic programming problem. It is also shown that if the direction is rest ricted to be a convex combination of the current subgradient and the p revious direction, then an optimal choice of stepsize and direction is equivalent to the Camerini-Fratta-Maffioli modification of the subgra dient method.