A New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming

Liang Fang

doi:10.24297/jam.v16i0.8152

Authors

Liang Fang Taishan University

DOI:

https://doi.org/10.24297/jam.v16i0.8152

Keywords:

Second-order cone programming, non-interior continuation method, interior-point method, smoothing function, Euclidean Jordan algebra

Abstract

Second-order cone programming has received considerable attention in the past decades because of its wide range of applications. Non-interior continuation method is one of the most popular and efficient methods for solving second-order cone programming partially due to its superior numerical performances. In this paper, a new smoothing form of the well-known Fischer-Burmeister function is given. Based on the new smoothing function, an inexact non-interior continuation algorithm is proposed. Attractively, the new algorithm can start from an arbitrary point, and it solves only one system of linear equations inexactly and performs only one line search at each iteration. Moreover, under a mild assumption, the new algorithm has a globally linear and locally Q-quadratical convergence. Finally, some preliminary numerical results are reported which show the effectiveness of the presented algorithm.

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Author Biography

Liang Fang, Taishan University

College of Mathematics and Statistics, Taishan University, 271021, Tai'an

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