Abstract. A class of combinatorial optimization problems over polyhedral- spherical sets is considered. The results of convex extensions theory are generalized to certain classes of functions defined on sphere-located and vertex-located sets. The original problem has been equivalently formulated as a mathematical programming problem with convex both objective function and functional constraints. A numerical illustration and possible applications of the results to solving combinatorial problems are given.

Keywords: combinatorial optimization problem, polyhedral-spherical set, continuous representation, convex extension.