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This paper is aimed at presenting a systematic survey of the existing nowdifferent formulations for the problem of projection of the origin of theEuclidean space onto the convex polyhedron (PPOCP). In the present paper, thereare investigated the reduction of the projection program to the problems ofquadratic programming, maximin, linear complementarity, and nonnegative leastsquares. Such reduction justifies the opportunity of utilizing a much morebroad spectrum of powerful tools of mathematical programming for solving PPOCP.  The paper's goal is to draw the attention of a wide range of research at thedifferent formulations of the projection problem, which remain largely unknowndue to the fact that the papers (addressing the subject of concern) arepublished even though on the adjacent, but other topics, or only in theconference proceedings.

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