Convex optimization

Abstract

This chapter helps the students to identify convex functions, convex sets, and convex optimization problems. It presents comparison between a convex and a non-convex function. The chapter discusses that there are three properties that are useful for defining and identifying convex functions. These include: the sum of two or more convex functions is also a convex function, the composition of a convex and an affine function is also a convex function, and the composition of a convex function with a convex non-decreasing function is also a convex function. The chapter also helps recognize when a problem has global optimum and unique solution. It examines duality theory for convex optimization problems. The chapter also presents common examples of convex functions, and helps the students to formulate and solve a dual problem.