Journal of Siberian Federal University. Mathematics & Physics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Sib. Fed. Univ. Math. Phys.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 2, Pages 160–172 (Mi jsfu745)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

DOI: https://doi.org/10.17516/1997-1397-2019-12-2-160-172

Full text: PDF file (147 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.6
Received: 09.07.2018
Received in revised form: 06.12.2018
Accepted: 16.01.2019
Language:

Citation: Louiza Derbal, Zakia Kebbiche, “Theoretical and numerical result for linear optimization problem based on a new kernel function”, J. Sib. Fed. Univ. Math. Phys., 12:2 (2019), 160–172

Citation in format AMSBIB
\Bibitem{DerKeb19}
\by Louiza~Derbal, Zakia~Kebbiche
\paper Theoretical and numerical result for linear optimization problem based on a new kernel function
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 2
\pages 160--172
\mathnet{http://mi.mathnet.ru/jsfu745}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-2-160-172}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000467247000003}


Linking options:
  • http://mi.mathnet.ru/eng/jsfu745
  • http://mi.mathnet.ru/eng/jsfu/v12/i2/p160

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. Derbal, Z. Kebbiche, “An efficient parameterized logarithmic kernel function for semidefinite optimization”, Acta Math. Appl. Sin.-Engl. Ser., 36:3 (2020), 753–770  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
    Number of views:
    This page:120
    Full text:70
    References:11

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021