The optimality conditions of a nonlinear second-order cone program
can be reformulated as a nonsmooth system of equations using a
projection mapping. This allows the application of nonsmooth Newton
methods for the solution of the nonlinear second-order cone program.
Conditions for the local quadratic convergence of these nonsmooth
Newton methods are investigated. Related conditions are also given
for the special case of a linear second-order cone program. An
interesting and important feature of these conditions is that
they do not require strict complementarity of the solution.