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Analysis of a non-interior continuation method for second-order cone programming

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Abstract

Based on the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, a non-interior continuation method is presented for solving the second-order cone programming (SOCP). Our algorithm reformulates the SOCP as a nonlinear system of equations and then applies Newton’s method to the perturbation of this system. The proposed algorithm does not have restrictions regarding its starting point and solves at most one linear system of equations at each iteration. Under suitable assumptions, the algorithm is shown to be globally and locally quadratically convergent. Some numerical results are also included which indicate that our algorithm is promising and comparable to interior-point methods.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Huanggang Normal University, Huangzhou, 438000, Hubei, China

    Xiaoni Chi

  2. Department of Mathematical Sciences, Xidian University, Xi’an, 710071, China

    Sanyang Liu

Authors
  1. Xiaoni Chi
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  2. Sanyang Liu
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Corresponding author

Correspondence to Xiaoni Chi.

Additional information

This research was partially supported by the National Science Foundation of China (Grant No. 60574075, 60674108) and Cross-century Talent Award by the Ministry of Education, China.

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Chi, X., Liu, S. Analysis of a non-interior continuation method for second-order cone programming. J. Appl. Math. Comput. 27, 47–61 (2008). https://doi.org/10.1007/s12190-008-0057-0

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  • DOI: https://doi.org/10.1007/s12190-008-0057-0

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