A brief introduction to mathematical optimization

This chapter provides a brief introduction to mathematical optimization. It discusses sets and functions concepts in mathematics. The chapter presents the information on norms that include Euclidean norm, Manhattan distance, and infinity-norm or uniform norm. It covers the example of global and local optimum of the mathematical optimization problems. The chapter provides the maximum and minimum values of continuous functions. It helps the students to solve unconstrained optimization problems, using the gradient method implemented in Python. The chapter shows how to find the optimum using the gradient, and provides a complete review of Lagrange multipliers. It also helps the students to solve equality-constrained optimization problems, using Newton's method implemented in Python. The chapter is also an excuse for presenting Python's features as programming and modeling language.