Methods for solving systems of linear and convex inequalities based on the Fejér principle

Abstract

The paper contains a brief review of the author’s results concerning the technique of constructing Fejér contraction mappings, which are used in iterative processes of solving linear and convex systems of inequalities as well as accompanying optimization problems. The general approach is based on the notion of M-Fejér step “p → q” defined by the property

$$ \left| {q - y} \right| < \left| {p - y} \right|,\forall y \in M $$

. This property (postulate) assumes the existence of a point p ∈ $\overline {convM}$ and of a proper sufficiently arbitrary point q. Some of the problems considered in the paper are illustrated by schemes reflecting the analytics of these problems.