On the optimal correction of infeasible systems of linear inequalities
type: Item
instance of: scholarly article
title: On the optimal correction of infeasible systems of linear inequalities
zbMATH Open document ID: 1482.90173
author: Hossein Moosaei
author: Milan Hladík
published in: Journal of Optimization Theory and Applications
publication date: 2021-08-18T00:00:00Z
review text: The purpose of this paper is to describe a method for correcting infeasible systems of linear inequality. Specifically, given a system \(Ax\leq b\), the algorithm aims to find a matrix \(A^*\) and a vector \(b^*\) such that \(A^*x\leq b^*\) is feasible, and the sum of the Fröbenius norms of \(A-A^*\) and \(b-b^*\) are minimised. The problem is investigated in depth: it is shown that it is NP-hard, optimality conditions are described (when the minimium is attained, which is not guaranteed), and the problem is reformulated as a parametric optimisation problem that can be used to design a trust-region algorithm. Each subproblem in this trust-region method is solved using SQP. In the final part of the paper, the results of numerical experiments are presented to demonstrate that the method is reasonably accurate and efficient.
reviewed by: Julien Ugon
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 7383047
zbMATH Keywords: systems of linear inequalities
zbMATH Keywords: infeasible problems
zbMATH Keywords: fractional programming problem
zbMATH Keywords: lower and upper bounds
zbMATH Keywords: SQP
describes a project that uses: GQTPAR
MaRDI profile type: Publication
full work available at URL: s10957-021-01868-1
OpenAlex ID: W3164337295
cites work: Optimization in medicine. Most papers based on the presentation at the workshop on optimization in medicine, Coimbra, Portugal, July 20--22, 2005
cites work: Connections between the total least squares and the correction of an infeasible system of linear inequalities
cites work: A framework for optimal correction of inconsistent linear constraints
cites work: On optimal zero-preserving corrections for inconsistent linear systems
cites work: A reformulation-linearization-convexification algorithm for optimal correction of an inconsistent system of linear constraints
cites work: On the Solution of the Tikhonov Regularization of the Total Least Squares Problem
cites work: On linear infeasibility arising in intensity-modulated radiation therapy inverse planning
cites work: Q3996569
cites work: Trust Region Methods
cites work: Linear and nonlinear programming.
cites work: The trust region subproblem and semidefinite programming*
cites work: Differential properties of the marginal function in mathematical programming
cites work: Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
cites work: Radii of solvability and unsolvability of linear systems
cites work: On the minimum norm solution of linear programs
cites work: An efficient method for optimal correcting of absolute value equations by minimal changes in the right hand side
cites work: Optimal error correction and methods of feasible directions
cites work: On the solution of a nonconvex fractional quadratic problem
cites work: A Newton method for linear programming
cites work: Q4326385
cites work: A finite newton method for classification
cites work: Introduction to Interval Analysis
cites work: Tikhonov regularization for infeasible absolute value equations
cites work: Computing a Trust Region Step
cites work: Minimum norm solution to the positive semidefinite linear complementarity problem
cites work: A short note on \(\min_{x\in \mathbb{R}^n}\frac{\| Ax-b\|^2}{1+\| x \| ^2}\)
cites work: Correcting an inconsistent set of linear inequalities by the generalized Newton method
cites work: Q4221106
cites work: A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem
cites work: An LP-based algorithm for the correction of inconsistent linear equation and inequality systems
cites work: Q3137900
DOI: 10.1007/S10957-021-01868-1
description: scientific article; zbMATH DE number 7383047