This article is cited in 3 papers

Theoretical and numerical result for linear optimization problem based on a new kernel function

Louiza Derbal, Zakia Kebbiche

Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas, Setif1, 19000, Algeria

Abstract: The propose of this paper is to improve the complexity results of primal-dual interior-point methods for linear optimization (LO) problem. We define a new proximity function for (LO) by a new kernel function wich is a combination of the classic kernel function and a barrier term. We present various proprieties of this new kernel function. Futhermore, we formilate an algorithm for a large-update primal-dual interior-point method (IPM) for (LO). It is shown that the iteration bound for large-update and smal-update primal-dual interior points methods based on this function is a good as the currently best know iteration bounds for these type of methods. This result decreases the gap between the practical behaviour of the large-update algorithms and their theoretical performance, which is an open problem.The primal-dual algorithm is implemented with different choices of the step size.
Numerical results show that the algorithm with practical and dynamic step sizes is more efficient than that with fixed (theoretical) step size.

Keywords: kernel function, interior point algorithms, linear optimization, complexity bound, primal-dual methods.

UDC: 517.6

Received: 09.07.2018
Received in revised form: 06.12.2018
Accepted: 16.01.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-2-160-172

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