Computational efficiency of the simplex embedding method in convex nondifferentiable optimization

The simplex embedding method for solving convex nondifferentiable optimization problems is considered. A description of modifications of this method based on a shift of the cutting plane intended for cutting off the maximum number of simplex vertices is given. These modification speed up the problem solution. A numerical comparison of the efficiency of the proposed modifications based on the numerical solution of benchmark convex nondifferentiable optimization problems is presented.