Some convergence properties of descent methods

Z. Wei, Liqun Qi, H. Jiang

Research output: Journal article publicationJournal articleAcademic researchpeer-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 languageEnglish
Pages (from-to)177-188
Number of pages12
JournalJournal of Optimization Theory and Applications
Volume95
Issue number1
DOIs
Publication statusPublished - 1 Jan 1997
Externally publishedYes

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

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