On minimizing the sum of a convex function and a concave function

Abstract

We consider here the problem of minimizing a particular subclass of quasidifferentiable functions: those which may be represented as the sum of a convex function and a concave function. It is shown that in an n-dimensional space this problem is equivalent to the problem of minimizing a concave function on a convex set. A successive approximations method is suggested; this makes use of some of the principles of ∈-steepest-descent-type approaches.

Translated from Russian at the International Institute for Applied Systems Analysis (IIASA), A-2361 Laxenburg, Austria.