ABSTRACT
This chapter provides convex functions and their applications to mathematical programming. It explains the basic definition and examples of a convex function. The chapter discusses a brief study of convex functions of a real variable and a brief calculus review for functions of several variables. It presents some basic results concerning the optimization of convex functions, and then deals with some of the popular generalizations of this topic and their applications. The chapter also presents some important results concerning the minimization and maximization of a convex function. The first result deals with the problem of minimizing a convex function of several variables over a convex set. The first result shows that when the function is convex any relative minimum is a global minimum. In general the problem of determining the minima or maxima of a function of several variables is difficult.
