Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 35–45 | Cite as

The Problem of Projecting the Origin of Euclidean Space onto the Convex Polyhedron



This paper is aimed at presenting a systematic exposition of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). We have concentrated on the convex polyhedron given as a convex hull of finitely many vectors of the space. We investigated the reduction of the projection program to the problems of quadratic programming, maximin, linear complementarity, and nonnegative least squares. Such reduction justifies the opportunity of utilizing a much more broad spectrum of powerful tools of mathematical programming for solving the PPOCP. The paper’s goal is to draw the attention of a wide range of research at the different formulations of the projection problem.

Keywords and phrases

projection convex polyhedron quadratic programming maximin problem complementarity problem nonnegative least squares problem 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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