Errors of gradient extrema of a strictly convex function of discrete argument

Abstract

Some properties of convex (on partially ordered sets) functions with bounded above finite difference operators, namely gradients which are discrete analogues of derivatives, are investigated. Some estimates of the proximity of global and gradient extrema of a convex function of discrete argument are obtained, which exploit the bounds for diagonal elements of the Hessian of the function and the parameters of the admissible domain.

Stability gradient algorithm on Jordan-Dedekind structures

“…Then, by repeating the scheme of the proof of Theorem 4 [4], we obtain estimates (1). Lemma is proved.…”

“…This point g x is called the gradient maximum the function ( ) f x on the set H[4].By a guaranteed error estimate for the gradient algorithm in Problem A we mean…”