Approximation of convex functions by projections of polyhedra

A method for approximate solution of minimization problems for multivariate convex functions with convex constraints is proposed in the paper. The main idea consists in approximation of the objective function and constraints by piecewise linear functions, then the problem of convex programming can be reduced to a problem of linear programming. We present algorithms for construction of approximating polygons for some classes of univariate convex functions. The many-dimensional problem is reduced to a one-dimensional one by an inductive procedure. The efficiency of the method is illustrated by numerical examples.