Combining a hybrid preconditioner and a optimal adjustment algorithm to accelerate the convergence of interior point methods

DOI10.1016/j.laa.2011.08.023zbMath1236.65065OpenAlexW2005457454MaRDI QIDQ665950

Juan-Miguel Gracia

Publication date: 7 March 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.08.023

zbMATH Keywords

linear programmingconvergence accelerationnumerical experimentspreconditioningconjugate gradient methodCholesky factorizationinterior point methodsnormal equation systemoptimal adjustment algorithm

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Interior-point methods (90C51)

Related Items (6)

A polynomial arc-search interior-point algorithm for linear programming ⋮ Switching preconditioners using a hybrid approach for linear systems arising from interior point methods for linear programming ⋮ Sparsity preserving preconditioners for linear systems in interior-point methods ⋮ Modified controlled Cholesky factorization for preconditioning linear systems from the interior-point method ⋮ A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods ⋮ Improving an interior-point approach for large block-angular problems by hybrid preconditioners

Uses Software

• PCx

Cites Work

• Unnamed Item
• Further development of multiple centrality correctors for interior point methods
• The effect of ordering on preconditioned conjugate gradients
• A new class of preconditioners for large-scale linear systems from interior point methods for linear programming
• Multiple centrality corrections in a primal-dual method for linear programming
• An implementation of Karmarkar's algorithm for linear programming
• Preconditioning indefinite systems in interior point methods for optimization
• Inexact constraint preconditioners for linear systems arising in interior point methods
• Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
• Using a hybrid preconditioner for solving large-scale linear systems arising from interior point methods
• A note on hybrid preconditioners for large-scale normal equations arising from interior-point methods
• A family of linear programming algorithms based on an algorithm by von Neumann
• An Implementation of Gaussian Elimination with Partial Pivoting for Sparse Systems
• On the Implementation of a Primal-Dual Interior Point Method
• On Implementing Mehrotra’s Predictor–Corrector Interior-Point Method for Linear Programming
• An improved incomplete Cholesky factorization
• An Efficient Solver for Multi--Right-Hand-Side Linear Systems Based on the CCCG($\eta$) Method with Applications to Implicit Time-Dependent Partial Differential Equations
• Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization
• PCx: an interior-point code for linear programming
• Constraint Preconditioning for Indefinite Linear Systems
• Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems
• On Best Conditioned Matrices

This page was built for publication: Combining a hybrid preconditioner and a optimal adjustment algorithm to accelerate the convergence of interior point methods