An interior point method for linear programming based on a class of Kernel functions

Interior point methods are not only the most effective methods for solving optimisation problems in practice but they also have polynomial time complexity. However, there is still a gap between the practical behavior of the interior point method algorithms and their theoretical complexity results. I...

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Bibliographic Details
Published inBulletin of the Australian Mathematical Society Vol. 71; no. 1; pp. 139 - 153
Main Authors Amini, K., Peyghami, M. R.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2005
Subjects
Algorithms
Complexity
Kernel functions
Linear programming
Mathematical analysis
Optimization
Polynomials
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ISSN0004-9727
1755-1633
1755-1633
DOI10.1017/S0004972700038090

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Summary:Interior point methods are not only the most effective methods for solving optimisation problems in practice but they also have polynomial time complexity. However, there is still a gap between the practical behavior of the interior point method algorithms and their theoretical complexity results. In this paper, by focusing on linear programming problems, we introduce a new family of kernel functions that have some simple and easy to check properties. We present a simplified analysis to obtain the complexity of generic interior point methods based on the proximity functions induced by these kernel functions. Finally, we prove that this family of kernel functions leads to improved iteration bounds of the large-update interior point methods.
Bibliography:istex:CB4A9D6739AF839F59D0237A9483526EE3CD390F
ArticleID:03809
PII:S0004972700038090
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ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0004-9727
1755-1633
1755-1633
DOI:10.1017/S0004972700038090