A smoothing-type Newton method for second-order cone programming problems based on a new smooth function

A new smoothing function similar with the well known Fischer-Burmeister function is given. Based on this new function, a smoothing-type Newton method is proposed for solving second-order cone programming. At each iteration, the proposed algorithm solves only one system of linear equations and performs only one line search. This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Preliminary numerical results demonstrate the effectiveness of the method.