SylabUZ
| Course name | Optimization methods |
| Course ID | 11.9-WE-AutD-OptimMeth-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | WIEiA - oferta ERASMUS / Automatic Control and Robotics |
| Education profile | - |
| Level of studies | Second-cycle Erasmus programme |
| Beginning semester | winter term 2018/2019 |
| Semester | 1 |
| ECTS credits to win | 6 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Laboratory | 30 | 2 | - | - | Credit with grade |
to familiarize students with the basic techniques of linear and nonlinear programming
to develop students' skills in the specification of optimization tasks in engineering design tasks and to solve them using numerical packages
Mathematical analysis, Linear algebra with analytical geometry, Numerical methods
Linear programming tasks (ZPL). Classic, standard, and canonical ZPL characters. The geometric method, base solutions, and simplex algorithm. Quotient programming. Transport and allocation problems.
Nonlinear programming (ZPN) tasks - conditions for optimality. Convex sets and functions. Necessary and sufficient conditions for the existence of an extreme function without restrictions. Lagrange multipliers method. Extrema of functions in the presence of equality and inequality constraints. Karush-Kuhn-Tucker conditions (KKT). The regularity of restrictions. Conditions for the existence of a saddle point. Square programming.
Computational methods for solving ZPN. Methods of searching the minimum towards Fibonacci methods, the golden ratio, Kiefer, Powell, and Davidon. Simple search methods: Hooke-Jeeves and Nelder-Mead methods. Continuous and discrete gradient algorithm. Newton's method. Gauss-Newton and Levenberg-Marquardt methods. Basic methods of improvement directions: Gauss-Seidel methods, fastest decrease, Fletcher-Reeves conjugate gradients, variable Davidon-Fletcher-Powell metrics. Searching for the minimum under restrictive conditions: methods of internal, external and mixed punishment, gradient projection method, sequential square programming method, methods of acceptable directions.
Basics of discrete and mixed optimization. Integer programming. Problems of shortest routes and maximum flow. Elements of dynamic programming.
Global Optimization. Stochastic optimization. Adaptive random search. Metaheuristic methods: simulated annealing algorithm, evolutionary algorithms, particle swarm optimization.
Multi-criteria optimization and adaptation in non-stationary environments. Paretooptymlaność. Types of non-stationary environments, classification of adaptive problems.
Practical issues. Simplification and elimination of restrictions. Elimination of discontinuities. Scaling the task. Numeric zooming of the gradient. Use of library procedures. Review of selected libraries of optimization procedures. Discussion of the methods implemented in popular numerical and symbolic processing systems.
wykład: wykład konwencjonalny
laboratorium: ćwiczenia laboratoryjne
| Outcome description | Outcome symbols | Methods of verification | The class form |
Wykład - warunkiem zaliczenia jest uzyskanie pozytywnej oceny z egzaminu przeprowadzonego w formie pisemnej lub ustnej
Laboratorium - warunkiem zaliczenia jest uzyskanie pozytywnych ocen ze wszystkich ćwiczeń laboratoryjnych, przewidzianych do realizacji w ramach programu laboratorium
Składowe oceny końcowej = wykład: 50% + laboratorium: 50%
Modified by dr hab. inż. Wojciech Paszke, prof. UZ (last modification: 29-04-2020 11:52)
