Regularization and normal solutions of systems of linear equations and inequalities
type: Item
instance of: scholarly article
title: Regularization and normal solutions of systems of linear equations and inequalities
zbMATH Open document ID: 1335.90066
DOI: 10.1134/S0081543815050090
author: A. I. Golikov
author: Yu. G. Evtushenko
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2015-08-20T00:00:00Z
review text: The paper provides unconstrained dual formulations of unconstrained optimization problems which arise from the regularization of the problems of solving a system of linear equations, a system of linear equations with nonnegativity constraints on the variables, and a system of linear inequalities. It is first shown that the regularized problem for a system of linear equations is equivalent to some constrained optimization problems as well as to a special least squares problem. By means of a theorem of the alternative the latter version of the problem allows the set-up of a dual problem which, in turn, can be equivalently stated as an unconstrained optimization problem. Then similar problems are shown to be dual ones for a system of linear equations with nonnegative variables and a system of linear inequalities. For each of these pairs of mutually dual problems, the solution of one of the problems can be easily computed from the solution of the other one so that the lower-dimensional problem of both may be solved in practice.
reviewed by: Rembert Reemtsen
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 6474028
zbMATH Keywords: system of linear equations
zbMATH Keywords: system of linear equations with nonnegativity constraints
zbMATH Keywords: regularized problem
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: quadratic function
zbMATH Keywords: piecewise quadratic function
zbMATH Keywords: dual problem
zbMATH Keywords: generalized Newton method
MaRDI profile type: Publication
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full work available at URL: s0081543815050090
OpenAlex ID: W2188486109
description: scientific article; zbMATH DE number 6474028