Proximal point type algorithms with relaxed and inertial effects beyond convexity

被引：1

作者：

Grad, S. -M. ^{[1
]}

Lara, F. ^{[2
]}

Marcavillaca, R. T. ^{[2
]}

机构：

[1] Inst Polytech Paris, Unite Math Appl, ENSTA Paris, Palaiseau, France

[2] Univ Tarapaca, Inst Alta Invest IAI, Arica, Chile

来源：

OPTIMIZATION | 2024年 / 73卷 / 11期

关键词：

Proximal point algorithms; relaxed iterative methods; inertial iterative methods; generalized convexity; prox-convexity; MAXIMAL MONOTONE-OPERATORS; WEAK-CONVERGENCE;

D O I：

10.1080/02331934.2024.2329779

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We show that the recent relaxed-inertial proximal point algorithm due to Attouch and Cabot remains convergent when the function to be minimized is not convex, being only endowed with certain generalized convexity properties. Numerical experiments showcase the improvements brought by the relaxation and inertia features to the standard proximal point method in this setting, too.

引用

页码：3393 / 3410

页数：18

共 50 条

[31] The Developments of Proximal Point Algorithms
Xing-Ju Cai
Ke Guo
Fan Jiang
Kai Wang
Zhong-Ming Wu
De-Ren Han
Journal of the Operations Research Society of China, 2022, 10 : 197 - 239
[32] Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space
Alvarez, F
SIAM JOURNAL ON OPTIMIZATION, 2004, 14 (03) : 773 - 782
[33] Revisit the over-relaxed proximal point algorithm
Huang, Zhenyu
Noor, Muhammad Aslam
APPLIED MATHEMATICS LETTERS, 2016, 62 : 55 - 62
[34] Alternated Inertial Fixed Point Algorithms
Matsushita, Shin-ya
MINIMAX THEORY AND ITS APPLICATIONS, 2024, 9 (02): : 357 - 376
[35] Convergence Rate of Inertial Proximal Algorithms with General Extrapolation and Proximal Coefficients
Attouch, Hedy
Chbani, Zaki
Riahi, Hassan
VIETNAM JOURNAL OF MATHEMATICS, 2020, 48 (02) : 247 - 276
[36] Convergence Rate of Inertial Proximal Algorithms with General Extrapolation and Proximal Coefficients
Hedy Attouch
Zaki Chbani
Hassan Riahi
Vietnam Journal of Mathematics, 2020, 48 : 247 - 276
[37] Convergence Analysis of the Over-relaxed Proximal Point Algorithms with Errors for Generalized Nonlinear Random Operator Equations
Cai, Lecai
Lan, Heng-you
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2013, 15 (07) : 1247 - 1256
[38] Proximal Point Algorithms with Inertial Extrapolation for Quasi-convex Pseudo-monotone Equilibrium Problems
Izuchukwu, Chinedu
Ogwo, Grace N.
Shehu, Yekini
NETWORKS & SPATIAL ECONOMICS, 2024, 24 (03): : 681 - 706
[39] On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems
Tan, Bing
Qin, Xiaolong
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2024, 50 (04)
[40] Relaxed inertial accelerated algorithms for solving split equality feasibility problem
Li, Meixia
Kao, Xiping
Che, Haitao
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (08): : 4109 - 4121

← 1 2 3 4 5 →