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A new wide neighborhood primal-dual second-order corrector algorithm for linear optimization

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Abstract

We propose a new large-step primal-dual second-order corrector interior-point method for linear optimization. At each iteration, our method uses the new wide neighborhood introduced by Darvay and Takács (Cent Eur J Oper Res 26(3):551–563, 2018. https://doi.org/10.1007/s10100-018-0524-0). In this paper we would like to improve the directions proposed by Darvay and Takács by adding a second-order corrector direction. The corrector step is multiplied by the square of the step length in the expression of the new iterate. To our best knowledge, this is the first primal-dual second-order corrector interior-point algorithm based on Darvay–Takács’s new wide neighborhood, which has the same complexity as the best short-step algorithms for linear optimization. Finally, numerical experiments show that the proposed algorithm is efficient and reliable.

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Acknowledgements

The first and the third author was supported by a Grant of the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0190, within PNCDI III. This research has been partially supported by the Hungarian Research Fund, 628 OTKA (grant no. NKFIH 125700). The research of Petra Renáta Rigó has been supported by the National Research, Development and Innovation Fund (TUDFO/51757/2019-ITM, Thematic Excellence Program).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, No. 1 Mihail Kogălniceanu Street, 400084, Cluj-Napoca, Romania

    Zsolt Darvay & Petra Renáta Rigó

  2. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Behrouz Kheirfam

  3. Department of Differential Equations, Budapest University of Technology and Economics, Budapest, Hungary

    Petra Renáta Rigó

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  1. Zsolt Darvay
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  2. Behrouz Kheirfam
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  3. Petra Renáta Rigó
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Correspondence to Zsolt Darvay.

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Darvay, Z., Kheirfam, B. & Rigó, P.R. A new wide neighborhood primal-dual second-order corrector algorithm for linear optimization. Optim Lett 14, 1747–1763 (2020). https://doi.org/10.1007/s11590-019-01468-z

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