A note on "A globally convergent BFGS method with nonmonotone line search for non-convex minimization"

被引：0

作者：

Zhang, Li ^{[1
]}

Chen, Xinlong ^{[1
]}

机构：

[1] Changsha Univ Sci & Technol, Dept Math, Changsha 410004, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 219卷 / 02期

关键词：

BFGS method; Nonmonotone line search; Global convergence;

D O I：

10.1016/j.amc.2012.06.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we point out that Assumptions 3.1, 3.2 in [Y. Xiao, H. Sun, Z. Wang, A globally convergent BFGS method with nonmonotone line search for non-convex minimization, J. Comput. Appl. Math. 230 (2009) 95-106] are not enough to guarantee the global convergence result Theorem 3.1 in [1]. We present a new assumption and show that the proposed method in [1] still converges globally under these three assumptions. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：764 / 766

页数：3

共 50 条

[31] Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems
Yang, Lei
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2024, 200 (01) : 68 - 103
[32] Non-convex clustering via proximal alternating linearized minimization method
Xie, Ting
Chen, Feiyu
[J]. INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2018, 16 (02)
[33] A Recursive Trust-Region Method for Non-Convex Constrained Minimization
Gross, Christian
Krause, Rolf
[J]. DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XVIII, 2009, 70 : 137 - 144
[34] Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values
Noll, Dominikus
[J]. COMPUTATIONAL AND ANALYTICAL MATHEMATICS: IN HONOR OF JONATHAN BORWEIN'S 60TH BIRTHDAY, 2013, 50 : 555 - 592
[35] Solving nonlinear programming problems with unbounded non-convex constraint sets via a globally convergent algorithm
Menglong Su
Jianhua Li
Zhonghai Xu
[J]. Journal of Inequalities and Applications, 2014
[36] Solving nonlinear programming problems with unbounded non-convex constraint sets via a globally convergent algorithm
Su, Menglong
Li, Jianhua
Xu, Zhonghai
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[37] Efficient Regret Minimization in Non-Convex Games
Hazan, Elad
Singh, Karan
Zhang, Cyril
[J]. INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 70, 2017, 70
[38] A globally convergent improved BFGS method for generalized Nash equilibrium problems
Singh A.
Ghosh D.
[J]. SeMA Journal, 2024, 81 (2) : 235 - 261
[39] Non-convex minimization -: The case of vector fields
Brüning, E
[J]. PARTIAL DIFFERENTIAL EQUATIONS AND SPECTRAL THEORY, 2001, 126 : 17 - 23
[40] A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization
Ming Li
Hongwei Liu
Zexian Liu
[J]. Numerical Algorithms, 2018, 79 : 195 - 219

← 1 2 3 4 5 →