A Class of Algorithms for Quadratic Minimization

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.