Accelerated derivative-free method for nonlinear monotone equations with an application

被引:19
|
作者
Ibrahim, Abdulkarim Hassan [1 ]
Kumam, Poom [1 ,2 ,3 ]
Abubakar, Auwal Bala [4 ,5 ]
Adamu, Abubakar [2 ,6 ]
机构
[1] King Mongkuts Univ Technol Thonburi KMUTT, KMUTTFixed Point Res Lab, Fixed Point Lab, Dept Math, Room SCL 802,Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand
[2] King Mongkuts Univ Technol Thonburi KMUTT, Ctr Excellence Theoret & Computat Sci TaCS CoE, Bangkok, Thailand
[3] China Med Univ, Dept Med Res, China Med Univ Hosp, Taichung, Taiwan
[4] Bayero Univ, Fac Phys Sci, Dept Math Sci, Kano, Nigeria
[5] Sefako Makgatho Hlth Sci Univ, Dept Math & Appl Math, Pretoria, South Africa
[6] African Univ Sci & Technol, Abuja, Nigeria
关键词
derivative-free method; inertial algorithm; iterative method; nonlinear equations; projection method; CONJUGATE-GRADIENT METHODS; PROJECTION METHOD; SUPERLINEAR CONVERGENCE; BFGS METHOD; ALGORITHM; OPTIMIZATION; EQUILIBRIUM; SYSTEMS;
D O I
10.1002/nla.2424
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three-term derivative-free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133-145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.
引用
收藏
页数:27
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