Kod przedmiotu: |
103B-ARxxx-MSA-EOPT |
Kod Erasmus / ISCED: |
(brak danych)
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(brak danych)
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Nazwa przedmiotu: |
Optimization Techniques |
Jednostka: |
Wydział Elektroniki i Technik Informacyjnych |
Grupy: |
( Courses in English )--eng.-EITI
( Przedmioty techniczne )---EITI
( Przedmioty zaawansowane )-Automatyka i robotyka-mgr.-EITI
( Przedmioty zaawansowane techniczne )--mgr.-EITI
( Technical Courses )--eng.-EITI
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Punkty ECTS i inne: |
(brak)
Podstawowe informacje o zasadach przyporządkowania punktów ECTS: - roczny wymiar godzinowy nakładu pracy studenta konieczny do osiągnięcia zakładanych efektów uczenia się dla danego etapu studiów wynosi 1500-1800 h, co odpowiada 60 ECTS;
- tygodniowy wymiar godzinowy nakładu pracy studenta wynosi 45 h;
- 1 punkt ECTS odpowiada 25-30 godzinom pracy studenta potrzebnej do osiągnięcia zakładanych efektów uczenia się;
- tygodniowy nakład pracy studenta konieczny do osiągnięcia zakładanych efektów uczenia się pozwala uzyskać 1,5 ECTS;
- nakład pracy potrzebny do zaliczenia przedmiotu, któremu przypisano 3 ECTS, stanowi 10% semestralnego obciążenia studenta.
zobacz reguły punktacji
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Język prowadzenia: |
angielski
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Jednostka decyzyjna: |
103000 - Wydział Elektroniki i Technik Informacyjnych
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Kod wydziałowy: |
EOPT
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Numer wersji: |
2
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Skrócony opis: |
(tylko po angielsku) The main objective of the course is to introduce its participants to the theory and solution methods for optimization problems in science and technology. The students will be able to: understand various theoretical and computational aspects of a wide range of optimization methods, realize the capabilities offered by various optimization methods, use of optimization toolboxes.
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Pełny opis: |
(tylko po angielsku) The main objective of the course is to introduce its participants to the theory and solution methods for optimization problems in science and technology. The students will be able to: understand various theoretical and computational aspects of a wide range of optimization methods, realize the capabilities offered by various optimization methods, use of optimization toolboxes.
Lecture contents Concepts and models of mathematical programming (4h): the concept of a mathematical model, modeling languages, types of problems of mathematical programming (optimization); examples of applications in engineering design, parameter identification, computer graphics; examples of mathematical model building; continuous and discrete optimization.
Linear programming (6h): standard form of linear programs, plyhedral set, vertices; basis matrix, basic solutions; geometry of the simplex method, simplex tableau, algorithms of the simplex method; two-phase simplex method; computational algorithms of the simplex method, revised simplex method, product form algorithms, degeneracy issues; optimality conditions and duality theory, dual simplex method, sensitivity analysis; nonsimplex algorithms.
Basic concepts and algorithms for (nonlinear) unconstrained optimization (4h): optimality conditions of the first and second order for differentiable unconstrained optimization; quadratic functions and quadratic local approximation; general algorithmic scheme with line search, convergence issues, review of linesearch methods; steepest descent; conjugate directions, quasi-Newton methods; direct (nongradient) search methods.
Theory of constrained optimization (4h): active constraints, feasible directions, polar cones, Farkas lemma, Karush-Kuhn-Tucker (KKT) conditions; linear case, convex problems, regularity conditions, saddle points of Lagrange function, duality theory.
Algorithms of nonlinear (constrained) programming (4h): methods of feasible directions, Zoutendijk algorithm; external and barrier penalty functions, Fiacco-McCormick method, multiplier methods based the augmented Lagrange function; elements of global optimization.
Discrete optimization (5h): review of typical mixed integer programming (MIP) and combinatorial optimization problems, use of integer variables to model logical relations, special structures in MIP problems; complexity of problems; variants of exact solutions methods, basic branch and bound methods, dynamic programming; approximation methods, sample heuristics and basic metaheuristics.
Multicriteria optimization (3h): concept of efficient solution, generation techniques, interactive methods.
Projects contents Project 1 (15h): Edition and analysis of examples of mathematical models with the use of either MATLAB or algebraic modeling languages such as AMPL, the selection and use of optimization algorithms from a library in order to perform given type of model analysis.
Project 2 (15h): Development and implementation of dedicated approaches to selected problem of nonlinear opimization or discrete optimization.
Similar Courses
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Literatura: |
(tylko po angielsku) - H.P. Williams, Model Building in Mathematical Programming, 5th
Ed, Wiley 2013.
- M.S. Bazaraa, J.J. Jarvis, H.D. Sherali, Linear Programming and
Network Flows, 4th Ed, Wiley, 2010.
- M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming,
Wiley, 2006.
- A.P. Ruszczyński, Nonlinear Optimization, Princeton Univ. Press,
2006.
- I.Maros, Computational Techniques of the Simplex Method, Kluwer,
2003.
- M.Ehrgott, Multicriteria Optimization, Springer, Berlin 2005.
- A.Kasperski, Discrete Optimization and Network Flows, Wroclaw
Univ. of Technology, 2011.
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Metody i kryteria oceniania: |
(tylko po angielsku) Theoretical knowledge is validated by means of an exam, scheduled for 2 hours and giving up to 60 points. Laborarories are assessed by laboratory tutors, giving up to 40 points. All points are summed up to produce a final mark:
A 91-110 points
B+ 81-90 points
B 71-80 points
C+ 61-70 points
C 51-60 points
D 0-50 points
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