Optimization

Relations:

During a review of study plans, the course A4B33OPT can be substituted for the course AE4B33OPT.

It is not possible to register for the course AE4B33OPT if the student is concurrently registered for or has already completed the course A4B33OPT (mutually exclusive courses).

It is not possible to register for the course AE4B33OPT if the student is concurrently registered for or has previously completed the course A4B33OPT (mutually exclusive courses).

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Cybernetics

Synopsis:

The course provides fundamentals of mathematical optimisation in finite dimensional (euclidean) spaces: linear programming incl. duality, least squares, optimality conditions for non-linear problems, convexity, basic numerical algorithms, dynamic programming.

Requirements:

Linear algebra, Calculus, Probability and statistics, Logic and graph theory

Syllabus of lectures:

1. Introduction to mathematical optimization.

2. Euclidean spaces, matices, linear mappings

3. The method of least squares

4. Singular value decomposition

5. Linear programming, simplex method, duality

6. Non-linear programming, optimality conditions

7. Numerical algorithms for unconstrained problems

8. Convex sets and convex functions

11. Convex optimisation tasks

12. Dynamic programming

Syllabus of tutorials:

The labs consist of theoretical exercises and practical assignments (homework). Programming language for practical assignments: MATLAB.

Study Objective:

Students will learn

- to recognise and formulate a problem as an optimisation problem with or without constraints

- necessary and sufficient optimality conditions

- fundamentals of convex analysis

- algorithms for solving optimisation problems

Study materials:

Textbook: „Boyd and Vanderberghe: Convex Optimization“ (freely available on www).

Lecture notes: will be available online after each lecture

Note:

URL: http://cw.felk.cvut.cz/doku.php/courses/ae4b33opt/start

Further information:

http://cw.felk.cvut.cz/doku.php/courses/ae4b33opt/start

No time-table has been prepared for this course

The course is a part of the following study plans: