An Active Set Method for Single-Cone Second-Order Cone Programs

We develop an active set method for solving second-order cone programs that may have an arbitrary number of linear constraints but are restricted to have only one second-order cone constraint. Problems of this form arise in the context of robust optimization and trust region methods. The proposed active set method exploits the fact that a second-order cone program with only one second-order cone constraint and no inequality constraints can be solved in closed form.