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A Line Search Penalty-Free Method for Nonlinear Second-Order Cone Programming

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Abstract

In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem is feasible. Besides that, it does not use penalty-function or filter technique. We first use a robust linear second-order cone programming subproblem to get a detective step and then compute an optimal step from a quadratic optimization subproblem. The search direction is a convex combination of the detective step and optimal step. This two-phase strategy and the penalty-free technique are employed to promote global convergence which is analyzed under mild assumptions. We report some numerical experiments whose results show that the proposed algorithm is applicable and efficient.

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Acknowledgement

The paper was written when the first author was at the University of Portsmouth as an academic visitor (February 2019–January 2020). The first author wishes to express his sincere thanks to Dr Chee Khian Sim for his advice and help. We would also like to thank the editor and the anonymous referees for their valuable and helpful comments that have improved the quality of this paper greatly.

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Authors and Affiliations

  1. Jiangsu University of Science and Technology, ZhenJiang, 212001, P.R. China

    Qi Zhao

  2. School of Mathematics Science, Soochow University, Suzhou, 215006, P.R. China

    Zhongwen Chen

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  1. Qi Zhao
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  2. Zhongwen Chen
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Correspondence to Zhongwen Chen.

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The work was supported by Chinese NSF grant 11871362 and Overseas Study Fund and Start-up Fund for doctoral research by JiangSu University of Science and Technology.

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Zhao, Q., Chen, Z. A Line Search Penalty-Free Method for Nonlinear Second-Order Cone Programming. Acta Appl Math 170, 291–317 (2020). https://doi.org/10.1007/s10440-020-00334-w

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