Newton-Type Method for Solving Systems of Linear Equations and Inequalities

被引：1
|
作者：
Golikov, A. I. [1 ,2 ]
Evtushenko, Yu. G. [1 ,2 ]
Kaporin, I. E. [1 ,2 ]
机构：
[1] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Dorodnitsyn Comp Ctr, Moscow 119333, Russia
[2] Natl Res Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2019年 / 59卷 / 12期
基金：
俄罗斯基础研究基金会;
关键词：
systems of linear equations and inequalities; regularization; penalty function method; duality; projection of a point; piecewise quadratic function; Newton's method; preconditioned conjugate gradient method;
D O I：
10.1134/S0965542519120091
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A Newton-type method is proposed for numerical minimization of convex piecewise quadratic functions, and its convergence is analyzed. Previously, a similar method was successfully applied to optimization problems arising in mesh generation. It is shown that the method is applicable to computing the projection of a given point onto the set of nonnegative solutions of a system of linear equations and to determining the distance between two convex polyhedra. The performance of the method is tested on a set of problems from the NETLIB repository.
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页码：2017 / 2032
页数：16
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