1. SylabUZ
2. Wydział Nauk Inżynieryjno-Technicznych
3. semestr zimowy 2021/2022
4. Automatyka i robotyka / Komputerowe Systemy Automatyki - Program Erasmus drugiego stopnia
5. Optimization methods

Wygeneruj PDF dla tej strony

Optimization methods - opis przedmiotu

Cel przedmiotu

• 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

Wymagania wstępne

Zapisz zmiany

Mathematical analysis, Linear algebra with analytical geometry, Numerical methods

Zakres tematyczny

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.

Metody kształcenia

Lecture, Laboratory exercises.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture – the main condition to get a pass is a positive evaluation of written or oral exam in the end of the semester.
Laboratory – the main condition to get a pass is a sufficient number of positive assessments of tests of theoretical preparing to each lab exercise and written reports of these exercises. The set of exercises is defined by the lecturer.

Calculation of the final grade: lecture 50% + laboratory 50%

Literatura podstawowa

1. Kukuła K.(red.): Badania operacyjne w przykładach i zadaniach, PWN, Warszawa, 2006
2. Bertsekas D.: Nonlinear programming, Athena Scientific, 2004
3. Ignasiak E.(red.): Badania operacyjne, PWN, Warszawa, 2001
4. Kusiak J., Danielewska-Tułecka A., Oprocha P.: Optymalizacja. Wybrane metody z przykładami zastosowań, PWN, 2009

Literatura uzupełniająca

1. Bertsekas D.: Convex Analysis and Optimization, Athena Scientific, 2003
2. Spall J.: Introduction to Stochastic Search and Optimization: Estimation, Simulation and Control, Wiley InterScience, 2003

Uwagi

Zmodyfikowane przez dr hab. inż. Wojciech Paszke, prof. UZ (ostatnia modyfikacja: 30-08-2021 10:50)