Optimization
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
AD4B33OPT | Z,ZK | 6 | 4+2c | Czech |
- 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, 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:
- Further information:
- http://cw.felk.cvut.cz/doku.php/courses/a4b33opt/start
- No time-table has been prepared for this course
- 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)