  In this work, we study the gradient projection method for solving a class of
stochastic control problems by using a mesh free approximation approach to
implement spatial dimension approximation. Our main contribution is to extend
the existing gradient projection method to moderate high-dimensional space. The
moving least square method and the general radial basis function interpolation
method are introduced as showcase methods to demonstrate our computational
framework, and rigorous numerical analysis is provided to prove the convergence
of our meshfree approximation approach. We also present several numerical
experiments to validate the theoretical results of our approach and demonstrate
the performance meshfree approximation in solving stochastic optimal control
problems.
