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Rigorous Error Bounds for Finite Dimensional Linear Programming Problems
Citation Link: https://doi.org/10.15480/882.488
Other Titles
Rigorose Fehlerschranken für endlich-dimensionale lineare Programme
Publikationstyp
Doctoral Thesis
Date Issued
2009
Sprache
English
Author(s)
Advisor
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2008-12-17
Institut
TORE-DOI
Citation
Christian Keil: Rigorous Error Bounds for Finite Dimensional Linear Programming Problems. Norderstedt: Books on Demand GmbH, 2009. , ISBN 9783837093353
This dissertation treats the theory, implementation, and application of rigorous error bounds in the context of finite dimensional linear programming problems.
Despite the theory of linear programming that is well understood and its numerous applications, commercial solvers frequently produce erroneous results for these problems. In contrast, verification methods yield solutions proved to be correct.
The thesis presents theorems that yield rigorous error bounds, a convergence analysis, and generalizations. The software package Lurupa is described, which offers the rigorous error bounds as a standalone software, a library, and from MATLAB. Extensive numerical experiments and a comparison with other software packages are presented. They demonstrate that exploiting the special structure of a problem is necessary when aiming for fast and reliable results.
Despite the theory of linear programming that is well understood and its numerous applications, commercial solvers frequently produce erroneous results for these problems. In contrast, verification methods yield solutions proved to be correct.
The thesis presents theorems that yield rigorous error bounds, a convergence analysis, and generalizations. The software package Lurupa is described, which offers the rigorous error bounds as a standalone software, a library, and from MATLAB. Extensive numerical experiments and a comparison with other software packages are presented. They demonstrate that exploiting the special structure of a problem is necessary when aiming for fast and reliable results.
Subjects
Rigorose Schranke, Softwarepaket
linear programming
rigorous error bounds
interval arithmetic
software
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