Some convergence properties of descent methods

Z. Wei; Liqun Qi; H. Jiang

doi:10.1023/A:1022691513687

Some convergence properties of descent methods

Z. Wei
, Liqun Qi
, H. Jiang

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

In this paper, we discuss the convergence properties of a class of descent algorithms for minimizing a continuously differentiable function f on Rnwithout assuming that the sequence {xk} of iterates is bounded. Under mild conditions, we prove that the limit infimum of ∥▽f(xk)∥ is zero and that false convergence does not occur when f is convex. Furthermore, we discuss the convergence rate of {∥xk∥} and {f(xk)} when {xk} is unbounded and {f(xk)} is bounded.

Original language	English
Pages (from-to)	177-188
Number of pages	12
Journal	Journal of Optimization Theory and Applications
Volume	95
Issue number	1
DOIs	https://doi.org/10.1023/A:1022691513687
Publication status	Published - 1 Jan 1997
Externally published	Yes

Keywords

Descent methods
Global convergence
Rate of convergence
Unconstrained differentiable minimization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

More information

10.1023/A:1022691513687

Cite this

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AB - In this paper, we discuss the convergence properties of a class of descent algorithms for minimizing a continuously differentiable function f on Rnwithout assuming that the sequence {xk} of iterates is bounded. Under mild conditions, we prove that the limit infimum of ∥▽f(xk)∥ is zero and that false convergence does not occur when f is convex. Furthermore, we discuss the convergence rate of {∥xk∥} and {f(xk)} when {xk} is unbounded and {f(xk)} is bounded.

KW - Descent methods

KW - Global convergence

KW - Rate of convergence

KW - Unconstrained differentiable minimization

UR - https://www.scopus.com/pages/publications/0031512550

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DO - 10.1023/A:1022691513687

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IS - 1

ER -

Some convergence properties of descent methods

Abstract

Keywords

ASJC Scopus subject areas

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