两类问题公共解集上的变分不等式解的算法
An Algorithm to Solve the Variational Inequality Problem Based on the Common Solutions of Two Classes of Problems
查看参考文献26篇
|
文摘
|
本文研究了Hilbert空间中求解分裂可行性问题和拟非扩张算子不动点问题的公共解的一种新算法,并在这两类问题公共解的基础上求解了变分不等式问题.与前人相比,增加了自适应的步长和惯性迭代算法,加快了算法生成的迭代序列的收敛速度.同时,将先前涉及的非扩张映射推广到拟非扩张映射,且在算法中加入了一个强正有界算子,将原来的黏性迭代算法推广到更一般的黏性迭代算法.在数值算例中验证了算法的有效性. |
|
其他语种文摘
|
We study a new algorithm to solve a common solution of the split feasibility problem and the fixed point problem involving quasi-nonexpansive mappings in Hilbert spaces.Based on the common solutions of these two classes of problems,we solve the variational inequality problem.Compared with the predecessors,the self-adaptive technique and the inertial iteration method are added,which can speed up the convergence rate of the iterative sequence generated by our algorithms.At the same time,we extend the involving previous nonexpansive mappings to extensive quasi-nonexpansive mappings.In addition,a strong positive bounded operator is added to the algorithm,which extends the original viscous iterative algorithm to a more general viscous iterative algorithm.The effectiveness of the algorithm is verified by numerical examples. |
|
来源
|
数学学报
,2024,67(4):704-718 【核心库】
|
|
DOI
|
10.12386/A20220171
|
|
关键词
|
惯性黏性迭代算法
;
拟非扩张算子
;
强正有界算子
;
变分不等式问题
;
分裂可行性问题
|
|
地址
|
1.
浙江广厦建设职业技术大学人文学院, 金华, 322100
2.
浙江师范大学数学科学学院, 金华, 321004
|
|
语种
|
中文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
0583-1431 |
|
学科
|
数学 |
|
基金
|
国家自然科学基金资助项目
|
|
文献收藏号
|
CSCD:7751742
|
参考文献 共
26
共2页
|
|
1.
Bot R I. An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems.
Numer. Algorithms,2016,71(3):519-540
|
CSCD被引
3
次
|
|
|
|
|
2.
Bot R I. Inertial Douglas-Rachford splitting for monotone inclusion problems.
Appl. Math. Comput,2015,256:472-487
|
CSCD被引
11
次
|
|
|
|
|
3.
Byrne C. Iterative oblique projection onto convex set and the split feasibility problem.
Inverse Probl,2002,18(2):441-453
|
CSCD被引
35
次
|
|
|
|
|
4.
Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction.
Inverse Probl,2004,20(1):103-120
|
CSCD被引
49
次
|
|
|
|
|
5.
Cai G. Viscosity iterative algorithms for a new variational inequality problem and fixed point problem in Hilbert spaces (in Chinese).
Acta Math. Sin. Chin. Ser,2019,62(5):765-776
|
CSCD被引
4
次
|
|
|
|
|
6.
Ceng L C. Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions.
Fixed Point Theory,2019,20(1):113-133
|
CSCD被引
1
次
|
|
|
|
|
7.
Censor Y. A multiprojection algorithm using Bregman projections in a product space.
Numer. Algorithms,1994,8(2/4):221-239
|
CSCD被引
48
次
|
|
|
|
|
8.
Chen C. Inertial proximal ADMM for linearly constrained separable convex optimization.
SIAM J. Imaging Sci,2015,8(4):2239-2267
|
CSCD被引
17
次
|
|
|
|
|
9.
Dong Q L. General splitting methods with linearization for the split feasibility problem.
J. Glob. Optim,2021,79(4):813-836
|
CSCD被引
4
次
|
|
|
|
|
10.
Hammad H A. Solving a split feasibility problem by the strong convergence of two projection algorithms in Hilbert spaces.
J. Funct. Space,2021,2021:5562694,11
|
CSCD被引
1
次
|
|
|
|
|
11.
He S. Solving the variational inequality problem defined on intersection of finite level sets.
Abstr. Appl. Anal,2013,2013:942315,8
|
CSCD被引
1
次
|
|
|
|
|
12.
Jiang B. Multi-step inertial regularized methods for hierarchical variational inequality problems involving generalized Lipschitzian mappings.
Mathematics,2021,9(17):2103,20
|
CSCD被引
1
次
|
|
|
|
|
13.
Kesornprom S. On the convergence analysis of the gradient-CQ algorithms for the split feasibility problem.
Numer. Algorithms,2020,84(3):997-1017
|
CSCD被引
3
次
|
|
|
|
|
14.
Kraikaew R. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces.
J. Optim. Theory Appl,2014,163(2):399-412
|
CSCD被引
7
次
|
|
|
|
|
15.
Lopez G. Solving the split feasibility problem without prior knowledge of matrix norms.
Inverse Probl,2012,28(8):085004,18
|
CSCD被引
12
次
|
|
|
|
|
16.
Marino G. A general iterative method for nonexpansive mappings in Hilbert spaces.
J. Math. Anal. Appl,2006,318(1):43-52
|
CSCD被引
24
次
|
|
|
|
|
17.
Polyak B. Some methods of speeding up the convergence of iteration methods.
Comput. Math. Math. Phys,1964,4(5):1-17
|
CSCD被引
67
次
|
|
|
|
|
18.
Qin X. A viscosity iterative method for a split feasibility problem.
J. Nonlinear Convex. Anal,2019,20(8):1497-1506
|
CSCD被引
1
次
|
|
|
|
|
19.
Tian M. Inertial modified Tseng's extragradient algorithms for solving monotone variational inequalities and fixed point problems.
J. Nonlinear Funct. Anal,2020,2020:35,19
|
CSCD被引
1
次
|
|
|
|
|
20.
Wang Y. A new algorithm for the common solutions of a generalized variational inequality system and a nonlinear operator equation in Banach spaces.
Mathematics,2020,8(11):1944,21
|
CSCD被引
1
次
|
|
|
|
|
了解气象卫星更多信息，请访问