- Department of Cybernetics
The course provides the basics of mathematical optimization: using linear algebra for optimization (least squares, SVD), Lagrange multipliers, selected numerical algorithms (gradient, Newton, Gauss-Newton, Levenberg-Marquardt methods), linear programming, convex sets and functions, intro to convex optimization, duality.
Linear algebra. Calculus, including intro to multivariate calculus. Recommended are numerical algorithms and probability and statistics.
- Syllabus of lectures:
1. General formulation of continuous optimization problems.
2. Matrix algebra. Linear and affine subspaces and mappings.
3. Orthogonality. QR decomposition.
4. Non-homogeneous linear systems: method of least squares and least norm.
5. Quadratic functions, spectral decomposition.
6. Singular value decomposition (SVD).
7. Non-linear mappings, their derivatives.
8. Analytical conditions on free extrema. Method of Lagrange multipliers.
9. Iterative algorithms for free local extrema: gradient, Newton, Gauss-Newton, Levenberg-Marquard method.
10. Linear programming: formulation and applications.
11. Convex sets and polyhedra.
12. Simplex method.
13. Duality in linear progrmaming.
14. Convex functions. Convex optimization problems.
15. Examples of non-convex problems.
- Syllabus of tutorials:
The labs consist of solving problems on blackboard and homeworks in Matlab.
Please see the course web page.
- Study Objective:
The aim of the course is to teach students to recognize optimization problems around them, formulate them mathematically, estimate their level of difficulty, and solve easier problems.
- Study materials:
See the course web page.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: