Course syllabus for Nonlinear optimisation

Linear algebra, analysis in one and several variables

The course is an introductory course in optimiza-tion. It serves to provide (1) basic knowledge of important classes of optimization problems and application areas of optimization models and methodologies; (2) practice in describing relevant parts of a real-world problem in a mathematical optimization model; (3) knowledge of and insights into the basic mathematical theory which underlies the principles of optimality; (4) examples of optimization methods that have been and can be developed from this theory in order to solve practical optimization problems.

Master the most important basic concepts in convex optimization, especially in convex analysis, and those in the related areas of duality and optimality. 

Be well aware of the basics of necessary and sufficient optimality conditions and be able to utilize this theory on concrete examples. 

Master the basics of linear optimization, especially within duality theory, and the most often utilized method for this problem class: the simplex method. 

Within nonlinear optimization master the notions of descent and feasible direction, and to be able to explain the principles behind classic methods such as steepest descent, variations of Newton's method, the Frank-Wolfe method, and sequential quadratic programming, and to be able to explain when they are expected to be convergent.

This basic course in optimization describes the most relevant mathematical principles that are used to analyze and solve optimization problems. The main theoretical goal is that You should understand parts of the theory of optimality, duality, and convexity, and their interrelations. In this way You will become able to analyze many types of optimization problems occurring in practice and both classify them and provide guidelines as to how they should be solved. This is the more practical goal of an otherwise mainly theoretical course.

Lectures, exercises, two computer exercises, and a project assignment that comprises mathematical modelling and the solution of a concrete optimization problem med industrial relevance. Additionally, there might be voluntary elements that could give bonus points for the written final exam.

"An Introduction to Continuous Optimization", by Niclas Andréasson, Anton Evgrafov, and Michael Patriksson, with Emil Gustavsson, Zuzana Nedělková, Kin Cheong Sou, and Magnus Önnheim, third edition, published by Studentlitteratur in 2016.

Project assignment (laboratory), computer exercises, a written final exam. There might be voluntary elements that could give bonus points for the written final exam.