A derivative-free scaling memoryless Broyden-Fletcher-Goldfarb-Shanno method for solving a system of monotone nonlinear equations

被引：23
|
作者：
Ullah, Najib [1 ]
Sabi'u, Jamilu [1 ]
Shah, Abdullah [1 ]
机构：
[1] COMSATS Univ Islamabad, Dept Math, Islamabad 45550, Pakistan
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2021年 / 28卷 / 05期
关键词：
global convergence; measure function; numerical comparison; projection technique; quasi‐ Newton methods; scaling memoryless BFGS update; QUASI-NEWTON METHODS; SCALED BFGS METHOD; GLOBAL CONVERGENCE; ALGORITHMS; FAMILY;
D O I：
10.1002/nla.2374
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents the two-parameter scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi-Newton method for ill-conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method. Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results.
引用
收藏
页数：17
相关论文
共 50 条
  • [21] A new derivative-free method for solving nonlinear equations
    Phiri, P. A.
    Makinde, O. D.
    INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, 2010, 5 (07): : 935 - 939
  • [22] A subspace inertial method for derivative-free nonlinear monotone equations
    Kimiaei, Morteza
    Ibrahim, Abdulkarim Hassan
    Ghaderi, Susan
    OPTIMIZATION, 2025, 74 (02) : 269 - 296
  • [23] A derivative-free projection method for solving convex constrained monotone equations
    Yuan, Na
    SCIENCEASIA, 2017, 43 (03): : 195 - 200
  • [24] A globally convergent derivative-free method for solving large-scale nonlinear monotone equations
    Yan, Qin-Rong
    Peng, Xiao-Zhen
    Li, Dong-Hui
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (03) : 649 - 657
  • [25] Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm
    Mwisomba, Candida
    Abdalla, Abdi T.
    Amour, Idrissa
    Mkemwa, Florian
    Maiseli, Baraka
    INTERNATIONAL JOURNAL OF MICROWAVE AND WIRELESS TECHNOLOGIES, 2022, 14 (06) : 739 - 749
  • [26] A derivative-free method for the system of nonlinear equations
    Nie, Pu-yan
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (03) : 378 - 384
  • [27] A three-term derivative-free projection method for nonlinear monotone system of equations
    Liu, J. K.
    Li, S. J.
    CALCOLO, 2016, 53 (03) : 427 - 450
  • [28] A three-term derivative-free projection method for nonlinear monotone system of equations
    J. K. Liu
    S. J. Li
    Calcolo, 2016, 53 : 427 - 450
  • [29] Inertial-Based Derivative-Free Method for System of Monotone Nonlinear Equations and Application
    Awwal, Aliyu Muhammed
    Kumam, Poom
    Wang, Lin
    Huang, Shuang
    Kumam, Wiyada
    IEEE ACCESS, 2020, 8 : 226921 - 226930
  • [30] A derivative-free iterative method for nonlinear monotone equations with convex constraints
    Jinkui Liu
    Yuming Feng
    Numerical Algorithms, 2019, 82 : 245 - 262
12345