A note on the global convergence theorem of accelerated adaptive Perry conjugate gradient methods

摘要

In Andrei (2017), a class of efficient conjugate gradient algorithms (ACGSSV) is proposed for solving large-scale unconstrained optimization problems. However, due to a wrong inequality and an incorrect reasoning used in analyzing the global convergence property for the proposed algorithm, the proof of Theorem 4.2, the global convergence theorem, is incorrect. In this paper, the necessary corrections are made. Under common assumptions, it is shown that Algorithm ACGSSV converges linearly to the unique minimizer.