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New method for determining search directions for interior-point algorithms in linear optimization

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Abstract

We introduce an interior-point algorithm for linear optimization, which is based on a new technique for determining search directions. This method consists of a new type of transformation on the centering equations of the system which characterizes the central path. It can be shown that these new directions cannot be derived from usual kernel functions. Therefore, we extend the concept of the kernel functions, and we establish an equivalence between this approach and the proposed method for obtaining search directions. Moreover, we prove the polynomial complexity of the algorithm.

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Acknowledgements

The authors are thankful for the valuable suggestions of the editor and the reviewers that helped improve the clarity and overall presentation of the paper. The authors are also grateful for the support of Edutus College (Collegium Talentum). This work was supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project Number PN-III-P4-ID-PCE-2016-0190.

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

    Zsolt Darvay & Petra-Renáta Takács

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  1. Zsolt Darvay
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Correspondence to Zsolt Darvay.

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Darvay, Z., Takács, PR. New method for determining search directions for interior-point algorithms in linear optimization. Optim Lett 12, 1099–1116 (2018). https://doi.org/10.1007/s11590-017-1171-4

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