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.