Optimization

Lecturer:

Tutor:

Supervisor:

Department of Cybernetics

Synopsis:

The course provides the basics of mathematical optimization: linear programming incl. duality, least squares, optimality conditions for non-linear problems, convexity, basic numerical algorithms, dynamic programming.

Requirements:

Linear algebra. Calculus, including intro to multivariate calculus. Recommended are numerical algorithms and probability and statistics.

Syllabus of lectures:

1. Introduction to mathematical optimization.

2. Review of neccessary parts of linear algebra

3. Eigen values and vectors, matrix decompositions

4. The method of least squares

5. Linear programming I: Geometry of LP

6. Linear programming II: Simplex method

7. Linear programming III: Duality

8. Review of selected parts from calculus

9. Non-linear programming: conditions for local extrema

10. Convex sets and convex functions

11. Examples of convex programming tasks

12. Numerical algorithms for unconstrained problems (gradient, Newton, Gauss-Newton, Leveberg-Marquardt method)

13. Dynamic programming

Syllabus of tutorials:

The labs consist of solving practically motivated problems. This

does not require lengthy coding but is mathematically nontrivial --

therefore preparation at home is necessary for each lab lesson. The MATLAB

programming language is used.

Here is <a href="https://cw.felk.cvut.cz/doku.php/courses/a4b33opt/cviceni/start">lab page </a> for the actual term.

Study Objective:

After the course, the students should be able to recognize optimization problems around them, formulate them mathematically, estimate their level of difficulty, and solve easier problems.

Study materials:

Selected parts of ČVUT FEL lecture notes „Jan Štecha: Optimální rozhodování a řízení“

Selected parts of the book „Boyd and Vanderberghe: Convex Optimization“ (freely available on www).

Here is <a href="https://cw.felk.cvut.cz/doku.php/courses/a4b33opt/start">lecture page</a> for the actual term.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Open Informatics - Computer Systems (compulsory course in the program)
• Open Informatics - Computer and Information Science (compulsory course in the program)
• Open Informatics - Software Systems (compulsory course in the program)
• Open Informatics (compulsory course in the program)