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

TL;DR

This paper systematically surveys various formulations of projecting the origin onto convex polyhedra, highlighting reductions to different optimization problems and advocating for broader use of mathematical programming tools.

Contribution

It provides a comprehensive overview of different formulations and reductions of the PPOCP, emphasizing underexplored approaches and unifying perspectives.

Findings

Reduction of PPOCP to quadratic programming, maximin, LCP, and nonnegative least squares

Demonstrates the potential of diverse mathematical programming tools for PPOCP

Highlights the need for broader research and dissemination of PPOCP formulations

Abstract

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.