A Weighted-Path-Following Interior-Point Algorithm for Second-Order Cone Optimization

Authors

Jingyong Tang, College of Mathematics and Information Science,Xinyang Normal University, Xinyang 464000, P. R. ChinaFollow
Li Dong, College of Mathematics and Information Science,Xinyang Normal University, Xinyang 464000, P. R. ChinaFollow
Liang Fang, College of Mathematics and System Science, Taishan University, Tai’an 271021, P. R. ChinaFollow
Jinchuan Zhou, Department of Mathematics, Shandong University of Technology, Zibo 255049, P. R. ChinaFollow

Author Country (or Countries)

P. R. China

Abstract

We present a weighted-path-following interior-point algorithm for solving second-order cone optimization. This algorithm starts from an initial point which is not on the central path. It generates iterates that simultaneously get closer to optimality and closer to centrality. At each iteration, we use only full Nesterov-Todd step; no line searches are required. We derive the complexity bound of the algorithm with small-update method, namely, O , where N denotes the number of second order cones in the problem formulation and e the desired accuracy. This bound is the currently best known iteration bound for second-order cone optimization.

Recommended Citation

Tang, Jingyong; Dong, Li; Fang, Liang; and Zhou, Jinchuan (2015) "A Weighted-Path-Following Interior-Point Algorithm for Second-Order Cone Optimization," Applied Mathematics & Information Sciences: Vol. 09: Iss. 2, Article 48.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss2/48