Course content

First and second order necessary and sufficient (Karush-Kuhn-Tucker) optimality conditions for unconstrained and constrained optimization problems in finite-dimensional vector spaces. Basics of convex analysis and Lagrangian duality theory and their application to optimization problems and algorithms. An overview of modern optimization techniques and algorithms for smooth problems (including line-search/trust-region, quasi-Newton, interior point and active set methods, SQP). Basic derivative-free and non-smooth optimization methods. Introduction to vector optimization.

Learning outcome

The student successfully meeting the learning objectives of the course will be able to:

1. assess the existence and uniqueness of solutions to a given optimization problem;
2. validate convexity of functions, sets, and optimization problems;
3. derive necessary and sufficient optimality conditions for a given optimization problem;
4. solve small optimization problems analytically;
5. explain the underlying principles and limitations of modern techniques and algorithms for optimization;
6. estimate the rate of convergence and complexity requirements of various optimization algorithms;
7. implement optimization algorithms on a computer;
8. apply optimization algorithms to model problems in engineering and natural sciences.

Learning methods and activities

Lectures, exercises and project. The final grade is composed of a written exam (70%) and a portfolio of project work (30%). Lectures will be given in English if international master or exchange students want to attend the course.

Recommended previous knowledge

Calculus 1-4, or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions