A link between the steepest descent method and fixed-point iterations

被引：2
|
作者：
Heid, Pascal [1 ]
机构：
[1] Univ Oxford, Math Inst, Woodstock Rd, Oxford OX2 6GG, England
来源：
OPTIMIZATION LETTERS | 2023年 / 17卷 / 01期
基金：
瑞士国家科学基金会;
关键词：
Fixed-point iterations; Steepest descent method; Preconditioned conjugate gradient method; Preconditioning operator; Sobolev gradient; CONVERGENCE CONDITIONS; NUMERICAL-SOLUTION; SOBOLEV GRADIENTS; MINIMIZATION; OPERATORS; SYSTEMS;
D O I：
10.1007/s11590-022-01867-9
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.
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页码：27 / 44
页数：18
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