ABSTRACT
This chapter introduces the most important properties of quadratic programming by means of geometrical examples. It focuses on 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. The chapter discusses the optimality conditions which are derived from geometrical considerations. It explains the geometry of quadratic functions is developed in terms of eigenvectors and eigenvalues. The chapter describes the nonconvex quadratic programming problems which are introduced geometrically; such problems may possess many local minima. It analyses the quadratic programming problem by observing properties of an optimal solution in several examples. The chapter distinguishes between convex and nonconvex quadratic programming problems and discusses some of the difficulties associated with the latter problem. Functions which are nonconvex may result in local optimal solutions which are different than the global optimal solution.
