Stability and accuracy of inexact interior point methods for convex quadratic programming
type: Item
instance of: scholarly article
title: Stability and accuracy of inexact interior point methods for convex quadratic programming
zbMATH Open document ID: 1381.65046
author: Benedetta Morini
author: Valeria Simoncini
published in: Journal of Optimization Theory and Applications
publication date: 2017-12-15T00:00:00Z
review text: Inexact interior point (IP) methods are procedures for linear, convex and nonlinear programming problems where the linear system arising at each iteration is solved approximately. This paper considers primal-dual IP methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. This work analyses the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation and different processes for retrieving the step after block elimination. The paper considers the sources of inexactness due either to roundoff and computational errors or to the iterative solution of the augmented system using typical procedures. If inexactness refers to roundoff errors, the presented theory recovers and extends some known results.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C51
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6819193
zbMATH Keywords: convex quadratic programming
zbMATH Keywords: primal-dual interior point methods
zbMATH Keywords: inexact interior point steps
zbMATH Keywords: iterative solution
zbMATH Keywords: roundoff errors
reviewed by: Nada Djuranović-Miličić
describes a project that uses: SparseMatrix
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: s10957-017-1170-8
OpenAlex ID: W2754060945
cites work: Inexact interior-point method
cites work: Large-Scale Scientific Computing
cites work: On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods
cites work: Convergence analysis of an inexact feasible interior point method for convex quadratic programming
cites work: Preconditioning indefinite systems in interior point methods for optimization
cites work: Local path-following property of inexact interior methods in nonlinear programming
cites work: On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems
cites work: Global convergence of the Newton interior-point method for nonlinear programming
cites work: Convergence analysis of the inexact infeasible interior-point method for linear optimization
cites work: Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation.
cites work: Interior Methods for Nonlinear Optimization
cites work: Q5691079
cites work: Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods
cites work: Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods
cites work: Stability of Symmetric Ill-Conditioned Systems Arising in Interior Methods for Constrained Optimization
cites work: Stability of Augmented System Factorizations in Interior-Point Methods
cites work: Effects of finite-precision arithmetic on interior-point methods for nonlinear programming
cites work: Stability of Linear Equations Solvers in Interior-Point Methods
cites work: Q4864704
cites work: A comparison of reduced and unreduced KKT systems arising from interior point methods
cites work: Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
cites work: Stopping criteria for inner iterations in inexact potential reduction methods: a computational study
cites work: Inexact Newton Methods
cites work: Krylov Subspace Methods
cites work: Q4902474
cites work: Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization
DOI: 10.1007/S10957-017-1170-8
description: scientific article; zbMATH DE number 6819193