ABSTRACT
This chapter reviews the basic mathematical tools that are useful for analyzing both unconstrained and constrained optimization problems. It provides three application examples to illustrate how it could apply the optimization techniques to solve real-world problems, with a focus on communications, networking, and signal processing. The chapter presents that several exercise questions are given to help the audience gain a deeper understanding of the material. One of the most fundamental problems in optimization is to derive conditions for identifying potential optimal solutions to an optimization problem. Typically, such conditions, which are known as optimality conditions, would enable people to reduce the original optimization problem to that of checking the validity of certain geometric conditions, or to that of checking the consistency of certain system of inequalities.
