New error bounds and their applications to convergence analysis of iterative algorithms

Authors
Citation
Zq. Luo, New error bounds and their applications to convergence analysis of iterative algorithms, MATH PROGR, 88(2), 2000, pp. 341-355
Citations number
42
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
0025-5610 → ACNP
Volume
88
Issue
2
Year of publication
2000
Pages
341 - 355
Database
ISI
SICI code
0025-5610(200008)88:2<341:NEBATA>2.0.ZU;2-5
Abstract
We present two new error bounds for optimization problems over a convex set whose objective function f is either semianalytic or gamma-strictly convex , with gamma greater than or equal to 1. We then apply these error bounds t o analyze the rate of convergence of a wide class of iterative descent algo rithms for the aforementioned optimization problem. Our analysis shows that the function sequence {f(x(k))} converges at least at the sublinear rate o f k(-epsilon) for some positive constant epsilon, where k is the iteration index. Moreover, the distances from the iterate sequence {x(k)} to the set of stationary points of the optimization problem converge to zero at least sublinearly.