Comments on "A three-term derivative-free projection method for nonlinear monotone system of equations"

被引：1

作者：

Liu, J. K. ^{[1
]}

Li, S. J. ^{[2
]}

机构：

[1] Chongqing Three Gorges Univ, Sch Math & Stat, Chongqing 404100, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 404100, Peoples R China

来源：

CALCOLO | 2017年 / 54卷 / 04期

关键词：

Nonlinear monotone equations; Derivative-free method; Conjugate gradient method; Projection method; Global convergence;

D O I：

10.1007/s10092-017-0224-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we show that the proof of Remark 3 of Lemma 3.2 in "A three-term derivative-free projection method for nonlinear monotone system of equations" (Calcolo 53:427-450, 2016) is not correct, which implies that the conclusion of Remark 3 is not appropriate to prove Theorem 3.1. A new proof of Remark 3 is established, which guarantees the corresponding global convergence Theorem 3.1. Throughout, we use the same notations and equation numbers as in the above reference.

引用

页码：1213 / 1215

页数：3

共 4 条

[1] Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations
Ahookhosh, Masoud
Amini, Keyvan
Bahrami, Somayeh
[J]. NUMERICAL ALGORITHMS, 2013, 64 (01) : 21 - 42
[2] A class of derivative-free methods for large-scale nonlinear monotone equations
Li, Qingna
Li, Dong-Hui
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (04) : 1625 - 1635
[3] A three-term derivative-free projection method for nonlinear monotone system of equations
Liu, J. K.
Li, S. J.
[J]. CALCOLO, 2016, 53 (03) : 427 - 450
[4] Solodov M.V., 1998, REFORMULATION NONSMO, P355, DOI DOI 10.1007/978-1-4757-6388-1_18

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