ON THE CONVERGENCE OF THE PROJECTED GRADIENT-METHOD

Authors
DUSSAULT JP FOURNIER G
Citation
Jp. Dussault et G. Fournier, ON THE CONVERGENCE OF THE PROJECTED GRADIENT-METHOD, Journal of optimization theory and applications, 77(1), 1993, pp. 197-208
Citations number
2
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
Journal title
Journal of optimization theory and applications → ACNP
ISSN journal
00223239
Volume
77
Issue
1
Year of publication
1993
Pages
197 - 208
Database
ISI
SICI code
0022-3239(1993)77:1<197:OTCOTP>2.0.ZU;2-Q
Abstract
We study the projected gradient algorithm for linearly constrained opt imization. Wolfe (Ref. 1) has produced a counterexample to show that t his algorithm can jam. However, his counterexample is only C1(R(n)), a nd it is conjectured that the algorithm is convergent for C2-functions . We show that this conjecture is partly right. We also show that one needs more assumptions to prove convergence, since we present a family of counterexamples. We finally give a demonstration that no jamming c an occur for quadratic objective functions.