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 $\mathrm{\parallel }x-p\mathrm{\parallel }$ for some $p\mathrm{\notin }P$. 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.