A feasible direction algorithm for nonlinear second-order cone programs

In this work, we present a new feasible direction algorithm for solving smooth nonlinear second-order cone programs. These consist of minimizing a nonlinear smooth objective function subject to some nonlinear second-order cone constraints. Given an interior point to the feasible set defined by the conic constraints, the algorithm generates a feasible sequence with monotone decreasing values of the objective function. Under mild assumptions, we prove the global convergence of the algorithm to KKT points. Finally, we present some computational results applied to several instances of randomly generated benchmark problems and robust support vector machine classification.