This article is cited in 1 paper

Universal extremum of hyperplanes in some optimization problems

N. P. Fedotova

P. G. Demidov Yaroslavl State University

Abstract: This paper is concerned with the minimum distance between a point and a polyhedrons of some class in the $R^n$ vector space supplied with different symmetrical norms. We find all hyperplanes where for all polyhedrons the point of Euclidean norm minimum is also one of the nearest points in any symmetrical norm. It simplifies the choice of criterion in some optimization problems.

Keywords: Norm, Euclidean norm, symmetrical norm, distance, hyperplane, class of hyperplanes, class of polyhedrons, $R^n$ space, optimization functions, optimization problems.

UDC: 517.972.9

Received: 28.05.2010