Introduction to Optimization
Postgraduate Course, AIMS, Cameroon, 2025
This course’s aim is to give an introduction into analytical and numerical methods for the solution of optimization problems in science and engineering. It is intended for students from mathematics, physics, engineering and computer science.
Course Content
The course’s focus is on continuous optimization with special emphasis on nonlinear programming. Besides nonlinear programming, we discuss important concepts from the field of convex optimization that we believe to be important to all users and developers of optimization methods. The course is divided into five major chapters.
Fundamental Concepts of Optimization
In This chapter, we introduce some Fundamental Concepts of Optimization and types of optimization problems.
Linear programming
In this chapter we study optimization problems with linear objective and constraint functions. We solve numerically in python as well as with the simplex method.
Constrained optimization problems
This chapter concerns Equality and inequality Constrained Optimization problems with KKT conditions. Key topics include the theory of first- and second-order optimality conditions, duality, and applications.
Iterative optimization Algorithms
In this chapter, we study gradient based methods of optimization and implement the algorithms in python.
Calculus of variation and Optimal Control
Next, we look at calculus of variation and end with optimal control theory. We shall illustrate the different concepts with examples to ease the understanding of the course.