ABSTRACT
This chapter develops the essential ideas of quadratic programming (QP). Section 5.1 shows how to solve a 2-dimensional QP by geometrical reasoning. In Section 5.2, optimality conditions are formulated for a QP, again using geometrical reasoning. In Section 5.3, it is shown how to draw elliptic level sets for a quadratic function. In Section 5.4, optimality conditions for a QP having n variables and m inequality constraints, are formulated and proven to be sufficient for optimality.
The purpose of this section is to introduce the most important properties of quadratic programming by means of geometrical examples. We first show how to determine an optimal solution geometrically. A major difference between linear and quadratic programming problems is the number of constraints active at an optimal solution and this is illustrated by means of several geometrical examples.
