A new non-interior continuation method for second-order cone programming

Abstract

- We propose a new smoothing function in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new function, we present a new noninterior continuation method for solving the second-order cone programming. We adopt a variant merit function. Our algorithm needs to solve only one system of linear equations and to perform only one line search at each iteration. It can start from an arbitrary point and does not require the iteration points to be in the set of strictly feasible solutions. We prove the global and local quadratic convergence of the algorithm under suitable assumptions. Numerical results indicate that our algorithm performs well.