ABSTRACT
This chapter describes the necessary and sufficient conditions for optimality for a quadratic minimization problem subject to linear equality constraints and to formulate an algorithm for the solution of this problem. It develops some basic concepts of quadratic functions which will be used for quadratic programme including Taylor's Theorem and a matrix updating formula. Taylor's series is an essential tool for analyzing a quadratic function. The chapter presents the notion of convexity, and gives necessary and sufficient conditions for an optimal solution of an unconstrained quadratic minimization problem. It provides an algorithm for the solution of the problem using conjugate directions and extends the results for quadratic minimization subject to linear equality constraints. It provides Matlab programs to implement each of the algorithms formulated. The chapter also presents the results of applying each algorithm to the text examples used to illustrate the algorithm.
