A MODIFIED LIU-STOREY-CONJUGATE DESCENT HYBRID PROJECTION METHOD FOR CONVEX CONSTRAINED NONLINEAR EQUATIONS AND IMAGE RESTORATION

被引：11

作者：

Ibrahim, Abdulkarim Hassan ^{[1
]}

Deepho, Jitsupa ^{[2
]}

Abubakar, Auwal Bala ^{[3
,4
]}

Aremu, Kazeem Olalekan ^{[5
]}

机构：

[1] King Mongkuts Univ Technol Thonburi KMUTT, Fac Sci, Dept Math, KMUTTFixed Point Res Lab,Room SCL 802 Fixed Point, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[2] King Mongkuts Univ Technol North Bangkok, Fac Sci Energy & Environm, 19 Moo 11, Amphur Bankhai 21120, Rayong, Thailand

[3] Bayero Univ, Dept Math Sci, Fac Phys Sci, Kano, Nigeria

[4] Sefako Makgatho Hlth Sci Univ, ZA-0204 Pretoria, Medunsa, South Africa

[5] Nigeria Sefako Makgatho Hlth Sci Univ, Usmanu Danfodiyo Univ Sokoto, Dept Math, ZA-0204 Pretoria, Medunsa, South Africa

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2022年 / 12卷 / 03期

关键词：

Nonlinear equations; Conjugate gradient method; Projection method; Global convergence; MONOTONE EQUATIONS; SUPERLINEAR CONVERGENCE; GRADIENT METHODS; BFGS METHOD; ALGORITHM; SYSTEMS;

D O I：

10.3934/naco.2021022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an iterative method for solving the convex constraint nonlinear equation problem. The method incorporates the projection strategy by Solodov and Svaiter with the hybrid Liu-Storey and Conjugate descent method by Yang et al. for solving the unconstrained optimization problem. The proposed method does not require the Jacobian information, nor does it require to store any matrix at each iteration. Thus, it has the potential to solve large-scale non-smooth problems. Under some standard assumptions, the convergence analysis of the method is established. Finally, to show the applicability of the proposed method, the proposed method is used to solve the l(1)-norm regularized problems to restore blurred and noisy images. The numerical experiment indicates that our result is a significant improvement compared with the related methods for solving the convex constraint nonlinear equation problem.

引用

页码：569 / 582

页数：14

共 45 条

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Abubakar A.B., 2020, APPL ANAL OPTIMIZATI, V4, P1

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