Approximate global minimization of nonconvex functions that are close to convex (Q1975077)

The authors consider a problem of the minimization of a nonconvex continuous function on a convex set. A special concept of closeness of this function to a convex function is introduced. This concept is illustrated by examples from various classes of nonconvex functions. When a nonconvex function to be minimized is close to a convex function, the original problem is approximated by the problems of the zero- and first-order approximation. For the optimal solutions of the latter problems, estimates of the accuracy of determining the global minimum in the original problem are obtained.