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Optimization and Engineering

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29-03-2019 | Research Article

An efficient primal-dual interior point method for linear programming problems based on a new kernel function with a finite exponential-trigonometric barrier term

Authors: S. Fathi-Hafshejani, M. Reza Peyghami, A. Fakharzadeh Jahromi

Published in: Optimization and Engineering | Issue 1/2020

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Abstract

In this paper, we first propose a new finite exponential-trigonometric kernel function that has finite value at the boundary of the feasible region. Then by using some simple analysis tools, we show that the new kernel function has exponential convexity property. We prove that the large-update primal-dual interior-point method based on this kernel function for solving linear optimization problems has \(O\left( \sqrt{n}\log n\log \frac{n}{\epsilon }\right)\) iteration bound in the worst case when the barrier parameter is taken large enough. Moreover, the numerical results reveal that the new finite exponential-trigonometric kernel function has better results than the other kernel functions.

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Title: An efficient primal-dual interior point method for linear programming problems based on a new kernel function with a finite exponential-trigonometric barrier term
Authors: S. Fathi-Hafshejani
M. Reza Peyghami
A. Fakharzadeh Jahromi
Publication date: 29-03-2019
Publisher: Springer US
Published in: Optimization and Engineering / Issue 1/2020
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI: https://doi.org/10.1007/s11081-019-09436-3

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