A Class of Algorithms for Quadratic Minimization

TL;DR

This paper introduces a class of algorithms designed to solve quadratic minimization problems by identifying the optimal face of a polyhedron for projection, with practical examples demonstrating their application.

Contribution

The paper proposes a new class of algorithms for quadratic minimization that efficiently find the optimal face of a polyhedron for projection, advancing solution methods in this area.

Findings

Algorithms successfully identify the correct face for projection

Methods are demonstrated through multiple example problems

Approach improves efficiency in quadratic minimization tasks

Abstract

Certain problems in quadratic minimization can be reduced to finding the point $x$ of a polyhedron ${ P}$ that minimizes the distance $\|x-p\|$ for some $p\notin { P}$. This amounts to a search for the appropriate face $F$ of ${ P}$ for which the minimizing point is the projection of $p$ onto $F$. We present a class of algorithms for finding the face $F$ and the corresponding minimizing point $x\in { P}$, then a number of examples using those methods.