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Type: Artigo de periódico
Title: A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming
Author: Gonzalez-Lima, MD
Oliveira, ARL
Oliveira, DE
Abstract: We introduce an efficient and robust proposal for solving linear systems arising at each iteration of primal-dual interior-point methods for linear programming. Our proposal is based on the stable system presented by Gonzalez-Lima et al. (Comput. Opt. Appl. 44:213-247, 2009). Using similar techniques as those employed in the splitting preconditioner introduced by Oliveira and Sorensen (Linear Algebra Appl. 394:1-24, 2005) we are able to express the stable system matrix in block form such that the diagonal blocks are nonsingular diagonal matrices and the off-diagonal blocks are matrices close to zero when the iterates are close to the solution set of the linear programming problem. For degenerate problems a perturbation of the diagonal is added. We use a low-cost fixed iterative method to solve this system. Numerical experiments have shown that our approach leads to very accurate solutions for the linear programming problem.
Subject: Linear programming
Primal-dual interior point methods
Linear systems
Country: EUA
Editor: Springer
Rights: fechado
Identifier DOI: 10.1007/s10589-013-9572-5
Date Issue: 2013
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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