Optimization

The course cannot be taken simultaneously with:

Optimization (A4B33OPT)

The course is a substitute for:

Optimization (A4B33OPT)

Garant předmětu:

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:

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: