A New Adaptive Subspace Minimization Three-Term Conjugate Gradient Algorithm for Unconstrained Optimization
Year: 2021
Author: Keke Zhang, Hongwei Liu, Zexian Liu
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 159–177
Abstract
A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper. The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces, and we also proposed an adaptive rule for choosing different searching directions at each iteration. We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition. With the used nonmonotone line search, we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions. Numerical experiments show that the proposed algorithm is promising for the given test problem set.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1907-m2018-0173
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 159–177
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Conjugate gradient method Nonmonotone line search Subspace minimization Sufficient descent condition Global convergence.