A one-step smoothing Newton method for second-order cone programming

Authors:
Xiaoni Chi;Sanyang Liu
Affiliations:
College of Mathematics and Information Science, Huanggang Normal University, Huangzhou 438000, Hubei, PR China;Department of Mathematical Sciences, Xidian University, Xi'an 710071, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

A new smoothing function for the second-order cone programming is given by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new function, a one-step smoothing Newton method is presented for solving the second-order cone programming. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. This algorithm does not have restrictions regarding its starting point and is Q-quadratically convergent. Numerical results suggest the effectiveness of our algorithm.