Optimization
Code  Completion  Credits  Range  Language 

AD4B33OPT  Z,ZK  7  28KP+6KC  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Cybernetics
 Synopsis:

The course provides the basics of mathematical optimization: using linear algebra for optimization (least squares, SVD), Lagrange multipliers, selected numerical algorithms (gradient, Newton, GaussNewton, LevenbergMarquardt methods), linear programming, convex sets and functions, intro to convex optimization, duality.
 Requirements:

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. Nonhomogeneous linear systems: method of least squares and least norm.
5. Quadratic functions, spectral decomposition.
6. Singular value decomposition (SVD).
7. Nonlinear mappings, their derivatives.
8. Analytical conditions on free extrema. Method of Lagrange multipliers.
9. Iterative algorithms for free local extrema: gradient, Newton, GaussNewton, LevenbergMarquard 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 nonconvex 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.
 Note:
 Further information:
 http://cw.felk.cvut.cz/doku.php/courses/b33opt/start
 No timetable has been prepared for this course
 The course is a part of the following study plans: