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In this project we work on the computation of shape restricted smoothing splines arising from statistics, engineering and science. We will formulate shape restricted smoothing splines as constrained optimal control problems of linear systems, subject to inequality initial state and control constraints. Since such a problem is inherently nonsmooth due to the constraints, several numerical methods from computational optimization will be exploited. One of such approaches is the active set method. We will discretize the continuous time optimal control problem and obtain a finite-dimensional optimization problem. An active set method will be exploited to compute discrete optimal solutions. Since a discretized problem is typically of large size, effective computation power (such as HPC) will be used. Convergence analysis will also performed for the proposed numerical method.