Implementation of an interior point method with basis preconditioning

  • The implementation of a linear programming interior point solver is described that is based on iterative linear algebra. The linear systems are preconditioned by a basis matrix, which is updated from one interior point iteration to the next to bound the entries in a certain tableau matrix. The update scheme is based on simplex-type pivot operations and is implemented using linear algebra techniques from the revised simplex method. An initial basis is constructed by a crash procedure after a few interior point iterations. The basis at the end of the interior point solve provides the starting basis for a crossover method which recovers a basic solution to the linear program. Results of a computational study on a diverse set of medium to large-scale problems are discussed.

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Metadaten
Author:Lukas Schork, Jacek Gondzio
DOI:https://doi.org/10.1007/s12532-020-00181-8
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2020
Tag:Software; Theoretical Computer Science
Volume:12
Issue:4
Page Number:33
First Page:603
Last Page:635
Mathematical Programming Computation :MPC 2020 - Issue 4
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