Hybrid algorithm for system of nonlinear monotone equations based on the convex combination of fletcher-reeves and a new conjugate residual parameters

Kamaluddeen Umar Danmalam, Hassan Mohammad*, Auwal Bala Abubakar, Aliyu Muhammed Awwal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, based on the projection strategy of Solodov and Svaiter (1998, Reformula-tion: Nonsmooth, Piecewise Smooth, Semismooth, and Smoothing Methods (M. Fukushima & L. Qi eds) Dordrecht: Kluwer, pp. 355-369), we present a hybrid conjugate residual algorithm for nonlinear monotone equations with convex constraints. The parameter is computed as a convex combination of the Fletcher-Reeves (FR) and a new conjugate residual parameters. Furthermore, the convex combination parameter is chosen in such a way that the search direction satisfied the descent property, independent of any line search. The global convergence of the proposed hybrid algorithm was given under some suitable conditions. The proposed approach is shown to be efficient and promising based on the preliminary computational experiments performed on some standard problems.

Original languageEnglish
Pages (from-to)2093-2106
Number of pages14
JournalThai Journal of Mathematics
Volume18
Issue number4
Publication statusPublished - Dec 2020
Externally publishedYes

Keywords

  • Computational results
  • Conjugate residual method
  • Global convergence
  • Large-scale problems
  • Nonlinear systems of equations

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