  The LP-Newton method solves the linear programming problem (LP) by repeatedly
projecting a current point onto a certain relevant polytope. In this paper, we
extend the algorithmic framework of the LP-Newton method to the second-order
cone programming problem (SOCP) via a linear semi-infinite programming (LSIP)
reformulation of the given SOCP. In the extension, we produce a sequence by
projection onto polyhedral cones constructed from LPs obtained by finitely
relaxing the LSIP. We show the global convergence property of the proposed
algorithm under mild assumptions, and investigate its efficiency through
numerical experiments comparing the proposed approach with the primal-dual
interior-point method for the SOCP.
