Exploiting damped techniques for nonlinear conjugate gradient methods

Mehiddin Al-Baali, Andrea Caliciotti, Giovanni Fasano, Massimo Roma

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we propose the use of damped techniques within Nonlinear Conjugate Gradient (NCG) methods. Damped techniques were introduced by Powell and recently reproposed by Al-Baali and till now, only applied in the framework of quasi-Newton methods. We extend their use to NCG methods in large scale unconstrained optimization, aiming at possibly improving the efficiency and the robustness of the latter methods, especially when solving difficult problems. We consider both unpreconditioned and Preconditioned NCG. In the latter case, we embed damped techniques within a class of preconditioners based on quasi-Newton updates. Our purpose is to possibly provide efficient preconditioners which approximate, in some sense, the inverse of the Hessian matrix, while still preserving information provided by the secant equation or some of its modifications. The results of an extensive numerical experience highlights that the proposed approach is quite promising.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalMathematical Methods of Operations Research
DOIs
Publication statusAccepted/In press - Jun 1 2017

Fingerprint

Conjugate gradient method
Conjugate Gradient Method
Damped
Preconditioner
Newton-Raphson method
Quasi-Newton
Large-scale Optimization
Quasi-Newton Method
Hessian matrix
Conjugate Gradient
Unconstrained Optimization
Chord or secant line
Update
Robustness
Gradient

Keywords

  • Damped techniques
  • Large scale unconstrained optimization
  • Nonlinear conjugate gradient methods
  • Quasi-Newton updates

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Management Science and Operations Research

Cite this

Exploiting damped techniques for nonlinear conjugate gradient methods. / Al-Baali, Mehiddin; Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo.

In: Mathematical Methods of Operations Research, 01.06.2017, p. 1-22.

Research output: Contribution to journalArticle

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