Solving the matrix nearness problem in the maximum norm by applying a projection and contraction method
type: Item
instance of: scholarly article
title: Solving the matrix nearness problem in the maximum norm by applying a projection and contraction method
zbMATH Open document ID: 1246.65095
DOI: 10.1155/2012/357954
published in: Advances in Operations Research
publication date: 2012-09-04T00:00:00Z
review text: Summary: Let \(S\) be a closed convex set of matrices and \(C\) be a given matrix. The matrix nearness problem considered in this paper is to find a matrix \(X\) in the set \(S\) at which max \(\{|x_{ij} - c_{ij}|\}\) reaches its minimum value. In order to solve the matrix nearness problem, the problem is reformulated to a min-max problem firstly, then the relationship between the min-max problem and a monotone linear variational inequality (LVI) is built. Since the matrix in the LVI problem has a special structure, a projection and contraction method is suggested to solve this LVI problem. Moreover, some implementing details of the method are presented in this paper. Finally, preliminary numerical results are reported, which show that this simple algorithm is promising for this matrix nearness problem.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 6076653
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/357954
OpenAlex ID: W2016668604
Wikidata QID: Q58698822
cites work: Public Key Cryptography – PKC 2004
cites work: Q4730687
cites work: Least-Squares Covariance Matrix Adjustment
cites work: Computing a nearest symmetric positive semidefinite matrix
cites work: Computing the nearest correlation matrix--a problem from finance
cites work: An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications
cites work: An Efficient Algorithm for Minimizing a Sum of p-Norms
cites work: Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
cites work: Matrix Nearness Problems with Bregman Divergences
cites work: A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming
cites work: A new method for a class of linear variational inequalities
cites work: Solving a class of linear projection equations
cites work: Q4865357
cites work: A class of projection and contraction methods for monotone variational inequalities
cites work: A class of linearized proximal alternating direction methods
cites work: On the basic theorem of complementarity
cites work: An improved prediction-correction method for monotone variational inequalities with separable operators
DBLP publication ID: journals/advor/XuS12
author: M. H. Xu
author: H. Shao
description: scientific article; zbMATH DE number 6076653