An optimal ordering scheme for the capacitated, finite-horizon, multi-period, multiproduct newsvendor problem was proposed by cite {shao06} using a hedging point policy. This solution requires the calculation of a central curve that divides the different ordering regions and a vector that defines the target inventory levels. The central curve is a nonlinear curve that determines the optimal order quantities as a function of the initial inventory levels. In this paper we propose a method for calculating this curve and vector using spline functions, infinitesimal perturbation analysis (IPA), and convex optimization. Using IPA the derivatives of the cost with respect to the variables that determine the spline function are efficiently calculated. A convex optimization algorithm is used to optimize the spline function, resulting in a optimal policy. We present the mathematical derivations and simulation results validating this solution.