
7
Quadratic Programming
7.1 Introduction
In this chapter, we consider a generalization of linear programming that in-
volves linear constraints, but the objective function is a quadratic function and
so will contain terms that involve the products of pairs of variables. Such an
optimization problem is called a quadratic programming (QP) problem and is
a very important class of problems as many applications can be modeled in this
framework. We illustrate the importance of quadratic programming through
financial portfolio applications. A characterization of optimality of quadratic
programs is given that will serve as the basis for algorithmic developmen ...