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An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

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Abstract

An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.

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Acknowledgements

The authors would like to thank the Associate Editor and one anonymous referee for their constructive comments and suggestions on the earlier version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, People’s Republic of China

    Liangshao Hou & Li-Zhi Liao

  2. Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Xun Qian

  3. JD Explore Academy, Beijing, People’s Republic of China

    Xun Qian

  4. Faculty of Science and Engineering, Curtin University, Perth, Australia

    Jie Sun

  5. School of Business, National University of Singapore, Singapore, Singapore

    Jie Sun

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  1. Liangshao Hou
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  2. Xun Qian
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  3. Li-Zhi Liao
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  4. Jie Sun
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Correspondence to Li-Zhi Liao.

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The work of L.-Z. Liao was supported in part by grants from General Research Fund (GRF) of Hong Kong. The work of J. Sun was partially supported by Australia Council Research under grant DP160102918.

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Hou, L., Qian, X., Liao, LZ. et al. An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming. J Sci Comput 90, 95 (2022). https://doi.org/10.1007/s10915-022-01765-3

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