FIXED-POINT QUASI-NEWTON METHODS

被引：11
|
作者：
MARTINEZ, JM
机构：
[1] Univ of Campinas, Campinas
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 1992年 / 29卷 / 05期
关键词：
QUASI-NEWTON METHODS; FIXED POINTS; NONLINEAR SYSTEMS; LEAST-CHANGE SECANT METHODS;
D O I：
10.1137/0729081
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article studies iterative methods defined by x(k+1) = PHI(x(k), E(k)), where X(k) is-an-element-of R(n) and E(k) lie on a space of parameters. Sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate. A theory of least-change secant update methods for this class of processes is developed. Several examples are given showing a wide range of applications of the new theory.
引用
收藏
页码：1413 / 1434
页数：22
相关论文
共 50 条
  • [1] Three-step fixed-point quasi-Newton methods for unconstrained optimisation
    Ford, JA
    Tharmlikit, S
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (07) : 1051 - 1060
  • [2] A QUASI-NEWTON METHOD FOR SOLVING FIXED-POINT PROBLEMS IN HILBERT-SPACES
    MORET, I
    OMARI, P
    NUMERISCHE MATHEMATIK, 1991, 59 (02) : 159 - 177
  • [3] Quasi-Newton Methods for Saddle Point Problems
    Liu, Chengchang
    Luo, Luo
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35, NEURIPS 2022, 2022,
  • [4] Resource Reduction of BFGS Quasi-Newton Implementation on FPGA using Fixed-Point Matrix Updating
    Liu, Jia
    Liu, Qiang
    2018 28TH INTERNATIONAL CONFERENCE ON FIELD PROGRAMMABLE LOGIC AND APPLICATIONS (FPL), 2018, : 301 - 306
  • [5] On quasi-Newton methods with modified quasi-Newton equation
    Xiao, Wei
    Sun, Fengjian
    PROCEEDINGS OF 2008 INTERNATIONAL PRE-OLYMPIC CONGRESS ON COMPUTER SCIENCE, VOL II: INFORMATION SCIENCE AND ENGINEERING, 2008, : 359 - 363
  • [6] A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization
    Chengxian Xu
    Jianzhong Zhang
    Annals of Operations Research, 2001, 103 : 213 - 234
  • [7] Survey of quasi-Newton equations and quasi-Newton methods for optimization
    Xu, CX
    Zhang, JZ
    ANNALS OF OPERATIONS RESEARCH, 2001, 103 (1-4) : 213 - 234
  • [8] QUASI-NEWTON METHODS FOR SADDLEPOINTS
    BIEGLERKONIG, F
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1985, 47 (04) : 393 - 399
  • [9] Stochastic Quasi-Newton Methods
    Mokhtari, Aryan
    Ribeiro, Alejandro
    PROCEEDINGS OF THE IEEE, 2020, 108 (11) : 1906 - 1922
  • [10] Quasi-Newton approaches to interior point methods for quadratic problems
    Gondzio, J.
    Sobral, F. N. C.
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2019, 74 (01) : 93 - 120
12345