A Preconditioner for Solving Linear Programming Problems With Dense Columns

doi:10.1002/nla.70063

Return

A Preconditioner for Solving Linear Programming Problems With Dense Columns

2026-02-01

Villalba, Catalina J. *

Aurelio R. L. Oliveira

DOI：10.1002/nla.70063

Original

Save

View PDF

Abstract

En 中文

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix of the linear programming problem includes dense columns. In this paper, we propose a preconditioner to handle linear programming problems with dense columns, and we prove theoretically that the final linear system to solve is uniformly bounded when the Interior-Point Method is converging to an optimal solution. This result is illustrated through computational experiments, which show that our proposed method is robust and competitive in terms of running time and/or number of iterations compared with existing methods.

Keywords:

dense columns

interior-point methods

linear programming

preconditioner

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.