We propose an SQP-type algorithm for solving
nonlinear second-order cone programming (NSOCP) problems.
At every iteration, the algorithm solves a
convex SOCP subproblem in which
the constraints involve linear approximations of the constraint
functions in the original problem and the objective function is
a convex quadratic function.
Those subproblems can be transformed into linear SOCP problems,
for which efficient interior point solvers are available.
We establish global convergence and local quadratic convergence of
the algorithm under appropriate assumptions.
We report numerical results to examine the effectiveness of the algorithm.