SylabUZ
Nazwa przedmiotu | Operational research |
Kod przedmiotu | 11.9-WE-INFD-OperRes-Er |
Wydział | Wydział Informatyki, Elektrotechniki i Automatyki |
Kierunek | WIEiA - oferta ERASMUS / Informatyka |
Profil | - |
Rodzaj studiów | Program Erasmus drugiego stopnia |
Semestr rozpoczęcia | semestr zimowy 2018/2019 |
Semestr | 1 |
Liczba punktów ECTS do zdobycia | 5 |
Typ przedmiotu | obowiązkowy |
Język nauczania | angielski |
Sylabus opracował |
|
Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
Wykład | 30 | 2 | - | - | Egzamin |
Laboratorium | 30 | 2 | - | - | Zaliczenie na ocenę |
Mathematical analysis, Linear algebra and analytic geometry
Linear programming tasks (LPT). Standard formulation of LPT. Method of elementary solutions and
simplex algorithm. Optimal choice for production assortment. Mixture problem. Technological process
choice. Rational programming. Transportation and assignment problems. Two-person zero sum games
and games with nature.
Network programming. Network models with determined logical structure. CPM and PERT methods. Timecost
analysis. CPM_COST and PERT-COST methods.
Non-linear programming tasks (NPT) – optimality conditions. Convex sets and functions. Necessary and
sufficient conditions for the solution existence in the case without constraints. Lagrange multiplayers
method. Extrema of the function with equality and inequality constraints. Kuhn-Tucker conditions.
Constraints regularity. Conditions of an equilibrium point existence. Least squares method. Quadratic
programming.
Computational methods for solving NPT. Directional search methods: Fibonacci, golden search, Kiefer,
Powell and Davidon. Method of basic search: Hooke-Jeeves and Nelder-Mead. Continuous and discrete
gradient algorithm. Newton method. Gauss-Newton and Levenberg-Marquardt algorithms. Elementary
methods of feasible direction: Gauss-Seidel, steepest decent, conjugate gradient of Fletcher-Reeves,
variable metric of Davidon-Fletcher-Powell. Searching for minimum in the case of constraints: internal,
external and mixed penalty functions, projected gradient, sequential quadratic programming and
admissible directions method. Elements of dynamic programming.
Practical issues. Simplification and elimination of constraints. Discontinuity elimination. Scaling.
Numerical approximation of gradient. Usage of numerical packages. Presentation of methods
implemented in popular environments for symbolic and numerical processing.
Lecture, laboratory exercises.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Lecture – the passing condition is to obtain positive mark from the exam;
Laboratory – the passing condition is to obtain positive marks from all laboratory exercises
to be planned within the laboratory schedule.
Calculation of the final grade: lecture 50% + laboratory 50%
1. Ferris M., Mangasarian O., Wright S.: Linear programming in MATLAB, Cambridge University Press, 2008.
2. Ravindran A., Philips D., Solberg J.: Operational research: Principles and Practice, Wiley, 1987.
3. Winston W.: Operations Research Applications and Algorithms, Wadsworth Publishing Company, 1997.
4. Hillier F., Lieberman G.: Introduction to operations research, McGraw-Hill College, 1995.
5. Bertsekas D.: Nonlinear programming, 2nd edition, Athena Scientific, 2004
6. Boyd S., Vandenberghe L.: Convex optimization, Cambridge University Press, 2004.
Zmodyfikowane przez dr hab. inż. Maciej Patan, prof. UZ (ostatnia modyfikacja: 31-03-2018 18:13)