SylabUZ
| Course name | Introduction to Optimization |
| Course ID | 11.1-WK-MATP-PO-W-S14_pNadGen5VUO9 |
| Faculty | Faculty of Mathematics, Computer Science and Econometrics |
| Field of study | Mathematics |
| Education profile | academic |
| Level of studies | First-cycle studies leading to Bachelor's degree |
| Beginning semester | winter term 2019/2020 |
| Semester | 5 |
| ECTS credits to win | 6 |
| Course type | optional |
| Teaching language | polish |
| 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 |
The lecture should give a general knowledge on mathematical foundation of optimization, in particular on necessary and sufficient optimality conditions, on basic optimization methods and appropriate software.
Linear algebra 1 and 2, mathematical analysis 1 and 2.
1. Backgrounds
Optimization problems and their classification. Various forms of optimization problems and the relationships among the problems. Elements of linear algebra, of differentiation and of convex analysis.
2. Optimality conditions
Basic optimality conditions. Necessary and sufficient optimality conditions of the first order and of the second order for unconstrained minimization. Convex optimization problem. Duality
3. Unconstrained minimization methods
Line search. General form of descent methods and their convergence. Methods: steepest descent, conjugate gradients, Newton, DFP and BFGS.
Traditional lecture, laboratory with application of appropriate software.
| Outcome description | Outcome symbols | Methods of verification | The class form |
1. Checking the activity of the student
2. Written tests
3. Checking the ability of application of an appropriate software
4. Written examination
The final grade consists of the lab’s grade (50%) and the examination’s grade (50%)
1. M. Brdyś, A. Ruszczyński, Metody optymalizacji w zadaniach, WNT, Warszawa, 1985.
2. A. Cegielski, Podstawy optymalizacji, skrypt do wykładu
3. W. Findeisen, J. Szymanowski, A. Wierzbicki, Teoria i metody obliczeniowe optymalizacji, PWN, Warszawa, 1980.
4. Z. Galas, I. Nykowski (red.), Zbiór zadań z programowania matematycznego, część I, II, PWN, Warszawa, 1986, 1988.
5. W. Grabowski, Programowanie matematyczne, PWE, Warszawa, 1980.
6. J. Stadnicki, Teoria i praktyka rozwiązywania zadań optymalizacji, WNT, Warszawa, 2006.
1. M. S. Bazaraa, H. D. Sherali, 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. J.E. Dennis, R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia 1996.
4. R. Fletcher, Practical Methods of Optimization, Vol I, Vol. II, John Willey, Chichester, 1980, 1981.
5. C. Geiger and Ch. Kanzow, Numerische Verfahren zur Lösung unrestingierter Optimierungsaufgaben, Springer - Verlag, Berlin, 1999.
6. C. Geiger and Ch. Kanzow, Theorie und Numerik restringierter Optimierungsaufgaben, Springer - Verlag, Berlin, 2002
Modified by dr Robert Dylewski, prof. UZ (last modification: 20-09-2019 10:02)
