Quadratic convergence of a non-interior continuation method for second-order cone programming

Based on the Chen-Harker-Kanzow-Smale smoothing function, a non-interior continuation method is proposed for solving the second-order cone programming. Unlike interior point methods, the proposed algorithm can start from an arbitrary point. Our algorithm solves only one linear system of equations and performs only one line search at each iteration. Without uniform nonsingularity, the algorithm is shown to be globally and locally quadratically convergent. Numerical results indicate that our algorithm is promising.