An upper bound on the number of local maxima in the problem of maximizing the norm of the vector on the convex set

Abstract

In this  paper we consider of nonlinear optimization multiextremal the problem. These problems are converted by the exact quadratic regularization to one-extremal or to the maximum norm of the vector on a convex set. Under this transformation, the number of local extreme is greatly reduced, there by simplifying the solution of the original problem. We have found an upper bound on the number of different local extreme transformed of multiextremal problem.