A large-update primal–dual interior-point algorithm for second-order cone optimization based on a new proximity function

Abstract

In this paper, we propose a large-update primal–dual interior-point algorithm for second-order cone optimization (SOCO) based on a class of kernel functions consisting of a trigonometric barrier term. The algorithm starts from a strictly feasible point and generates a sequence of points converging to an optimal solution of the problem. Using a simple analysis, we show that the algorithm has worst case iteration complexity for large-update primal–dual interior point methods which coincides with the so far best-known iteration bound for SOCO.

Keywords:

• Second-order cone optimization problem
• primal–dual interior-point methods
• kernel function

Acknowledgements

The authors would like to thank the Research Council of K.N. Toosi University of Technology and Shahrekord University for supporting the work. The second author would like to thank for the financial grant from Shahrekord University. The second author was also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.

Notes

No potential conflict of interest was reported by the authors.