  This paper is aimed at presenting a systematic survey of the existing now
different formulations for the problem of projection of the origin of the
Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there
are 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 PPOCP.
  The paper's goal is to draw the attention of a wide range of research at the
different formulations of the projection problem, which remain largely unknown
due to the fact that the papers (addressing the subject of concern) are
published even though on the adjacent, but other topics, or only in the
conference proceedings.
