Optimization

Lecturer:

Tomáš Werner (gar.), Vojtěch Franc

Tutor:

Tomáš Werner (gar.), Vojtěch Franc, Jan Heller, Daniel Průša, Karel Zimmermann

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

Study materials:

See the course home page https://cw.felk.cvut.cz/doku.php/courses/a4b33opt/start

Note:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomKN:E-132 Franc V. 09:15–10:45 (lecture parallel1 parallel nr.101) Karlovo nám. Laboratoř PCroomKN:E-132 Heller J. 11:00–12:30 (lecture parallel1 parallel nr.102) Karlovo nám. Laboratoř PC
Tue	roomT2:C3-340 Werner T. Franc V. 12:45–14:15 (lecture parallel1) Dejvice Posluchárna
Fri
Thu	roomKN:E-132 Zimmermann K. 16:15–17:45 (lecture parallel1 parallel nr.106) Karlovo nám. Laboratoř PCroomKN:E-132 Heller J. 18:00–19:30 (lecture parallel1 parallel nr.104) Karlovo nám. Laboratoř PC
Fri	roomKN:E-132 Průša D. 07:30–09:00 (lecture parallel1 parallel nr.103) Karlovo nám. Laboratoř PCroomKN:E-107 Werner T. Franc V. 09:15–10:45 (lecture parallel1) Karlovo nám. Zengerova posluchárna K1roomKN:E-132 Průša D. 11:00–12:30 (lecture parallel1 parallel nr.105) Karlovo nám. Laboratoř PC

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Otevřená informatika - Počítačové systémy (compulsory course in the program)
• Otevřená informatika - Informatika a počítačové vědy (compulsory course in the program)
• Otevřená informatika - Softwarové systémy (compulsory course in the program)
• Otevřená informatika - před rozřazením do oborů (compulsory course in the program)