Description:

Systematic application of Matlab optimization toolbox for the solution of linear, quadratic, binary, integer an nonlinear programming tasks. Simulation of chaotic systems an fractal set generation.
Analysis of trajectories, attractors and fractal sets including estimation of their properties.

Contents:

1 Linear programming and related tasks in Matlab
2 Quadratic programming and related tasks in Matlab
3 Binary and integer programming and related tasks in Matlab
4 Nonlinear programming in Matlab
5 Penalization techniques and nonlinear optimization
6 Nonlinear regression and robust identification as optimization tasks
7 Discrete and continuous dynamic systems, simulation approaches and problems
8 Chaotic and turbulent systems in 1D
9 Trajectory and attractor
10 Lyapunov exponent estimation and power spectrum of chaotic trajectory
11 Deterministic fractal and similarity dimension
12 Fractal as result of stochastic modelling
13 Attractor as fractal set
14 Estimation of capacity, information and correlation dimensions

Seminar contents:

1 Linear programming and related tasks in Matlab
2 Quadratic programming and related tasks in Matlab
3 Binary and integer programming and related tasks in Matlab
4 Nonlinear programming in Matlab
5 Penalization techniques and nonlinear optimization
6 Nonlinear regression and robust identification as optimization tasks
7 Discrete and continuous dynamic systems, simulation approaches and problems
8 Chaotic and turbulent systems in 1D
9 Trajectory and attractor
10 Lyapunov exponent estimation and power spectrum of chaotic trajectory
11 Deterministic fractal and similarity dimension
12 Fractal as result of stochastic modelling
13 Attractor as fractal set
14 Estimation of capacity, information and correlation dimensions

Recommended literature:

Key references:
Sierkisma G.: Linear and Integer Programming, Marcel Dekker, 2002.
Dostal Z.: Optimal Quadratic Programming Algorithms, Springer, 2009.
Recommended references:
Moler C.: Numerical Computing with Matlab, SIAM, 2004.
Baker G.L., Golub J.P.: Chaotic Dynamics, Cambridge University Press, 1998.

Keywords:

Matlab, optimization, dynamic systems, chaos, fractal sets, analysis, parameter estimation

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar