An alternating direction method for second-order conic programming

An alternating direction dual augmented Lagrangian method for second-order cone programming (SOCP) problems is proposed. In the algorithm, at each iteration it first minimizes the dual augmented Lagrangian function with respect to the dual variables, and then with respect to the dual slack variables while keeping the other two variables fixed, and then finally it updates the Lagrange multipliers. Convergence result is given. Numerical results demonstrate that our method is fast and efficient, especially for the large-scale second-order cone programming.