Proposed is a novel iterative method for solving semi\-def\-inite programs. It exploits the ideology of cutting hyperplane through the center of mass of a convex body. To estimate the center of mass, we use a random walk technique known as the Hit-and-Run algorithm. The results of numerical simulations are compared to those obtained with presently available approaches. Robust versions of the method are considered, where the coefficient matrices contain norm-bounded uncertainties.