1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Introduction to Optimization

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Introduction to Optimization - opis przedmiotu

Cel przedmiotu

Students become familiar with the mathematical foundations of optimization, in particular the necessary and sufficient conditions for optimality. Moreover, students will learn basic methods of solving optimization problems and become familiar with the appropriate software.

Wymagania wstępne

Zapisz zmiany

Linear Algebra 1 and 2, Calculus 1 and 2

Zakres tematyczny

1. Introductory information. Optimization tasks. Classification. Various optimization problems and the relationships between them. Elements of linear algebra, differentiation and convex analysis.

2. Conditions for the existence of a minimum. Basic conditions for the existence of a minimum. Kuhn-Tucker conditions and order II conditions. Convex optimization. Duality.

3. Minimization without constraints. Exact and approximate directional minimization. The general form of descent methods and the conditions for their convergence. Methods: the fastest descent, conjugate gradients, Newton, DFP and BFGS.

Metody kształcenia

Traditional lecture; a laboratory in which students solve tasks and become familiar with software used to solve simple tasks optimization

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture: written exam consisting of test questions and tasks, verifying understanding of models and methods.

Laboratory: checking the level of students' preparation and their activity during classes; colloquium with tasks of varying difficulty; checking if the student knows how to use appropriate software

The course grade consists of the laboratory grade (50%) and the exam grade (50%).

The condition for passing the course is positive grades in the laboratory and exam.

Literatura podstawowa

1. M. S. Bazaraa, H.D. Sherali and  C.M. Shetty, Nonlinear Programming, Third Edition, J. Wiley&Sons, Hoboken, NJ, 2006

2. D.P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, MA, 1995

3. S. Boyd and L. Vandenberge,  Convex Optimization, Cambridge University Press, Cambridge 2004.

4. J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia 1996.

5. R. Fletcher, Practical Methods of Optimization, Vol I, Vol. II, John Willey, Chichester, 1980, 1981.

6. C. Geiger and Ch. Kanzow, Numerische Verfahren zur Lösung unrestingierter Optimierungsaufgaben, Springer-Verlag, Berlin, 1999.

7. C. Geiger and Ch. Kanzow, Theorie und Numerik restringierter Optimierungsaufgaben, Springer-Verlag, Berlin, 2002.

8. P.E. Gill, W. Murray and M.H. Wright, Practical Optimization, Academic Press, London 1981.

9. J. Nocedal and S.J.Wright, Numerical Optimization, Second Edition, Springer, 2006.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez prof. dr hab. Andrzej Cegielski (ostatnia modyfikacja: 28-12-2023 18:52)