A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

Wumei Sun (), Hongwei Liu () and Zexian Liu ()
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Wumei Sun: Xidian University
Hongwei Liu: Xidian University
Zexian Liu: Guizhou University

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 3, No 4, 840 pages

Abstract: Abstract The subspace minimization conjugate gradient methods based on Barzilai–Borwein method (SMCG_BB) and regularization model (SMCG_PR), which were proposed by Liu and Liu (J Optim Theory Appl 180(3):879–906, 2019) and Zhao et al. (Numer Algorithm, 2020. https://doi.org/10.1007/s11075-020-01017-1), respectively, are very interesting and efficient for unconstrained optimization. In this paper, two accelerated subspace minimization conjugate gradient methods are proposed for unconstrained optimization. Motivated by the subspace minimization conjugate gradient methods and the finite termination of linear conjugate gradient methods, we derive an acceleration parameter by the quadratic interpolation function to improve the stepsize, and the modified stepsize may be more closer to the stepsize obtained by exact line search. Moreover, several specific acceleration criteria to enhance the efficiency of the algorithm are designed. Under standard conditions, the global convergence of the proposed methods can be guaranteed. Numerical results show that the proposed accelerated methods are superior to two excellent subspace minimization conjugate gradient methods SMCG_BB and SMCG_PR.

Keywords: Conjugate gradient method; Regularization model; Barzilai–Borwein method; Subspace minimization; Acceleration method; 90C30; 90C06; 65K05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01897-w

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