CONVERGENCE OF THE STEEPEST DESCENT METHOD FOR MINIMIZING QUASI-CONVEX FUNCTIONS

Authors
KIWIEL KC MURTY K
Citation
Kc. Kiwiel et K. Murty, CONVERGENCE OF THE STEEPEST DESCENT METHOD FOR MINIMIZING QUASI-CONVEX FUNCTIONS, Journal of optimization theory and applications, 89(1), 1996, pp. 221-226
Citations number
14
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
Journal title
Journal of optimization theory and applications → ACNP
ISSN journal
00223239
Volume
89
Issue
1
Year of publication
1996
Pages
221 - 226
Database
ISI
SICI code
0022-3239(1996)89:1<221:COTSDM>2.0.ZU;2-O
Abstract
To minimize a continuously differentiable quasiconvex function f: R(n) -->R, Armijo's steepest descent method generates a sequence x(k+1)=x(k )-t(k) del f(x(k)), where t(k)>0. We establish strong convergence prop erties of this classic method: either x(k)-->(x) over bar, s.t. del f( (x) over bar)=0; or arg min f=empty set, parallel to x(k) parallel to- ->infinity, and f(x(k))down arrow inf f. We also discuss extensions to other line searches.