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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.

Based on the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, a non-interior continuation method is presented for solving the second-order cone programming (SOCP). Our algorithm reformulates the SOCP as a nonlinear system of equations and then applies Newton's method to the perturbation of this system. The proposed algorithm does not have restrictions regarding its starting point and solves at most one linear system of equations at each iteration. Under suitable assumptions, the algorithm is shown to be globally and locally quadratically convergent. Some numerical results are also included which indicate that our algorithm is promising and comparable to interior-point methods.

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