1. SylabUZ
2. Faculty of Mathematics, Computer Science and Econometrics
3. winter term 2019/2020
4. Mathematics - Second-cycle studies leading to MS degree
5. Mathematical Programming

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Mathematical Programming - course description

Aim of the course

The lecture should give a knowledge on methods for constrained minimization, in particular on methods for linear programming and quadratic programming. Furthermore, the lecture contains foundations of multicriterial and nondifferentiable minimization. In the laboratory the students apply an appropriate software.

Prerequisites

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Linear algebra 1 and 2, mathematical analysis 1 and 2, foundations of optimization.

Scope

1. Linear programming. Linear programming (LP) problems and problems which can be reduced to LP. Graphic method. Simplex algorithm, I and II phase. Duality in LP and the dual simplex algorithm.
2. Quadratic programming. Methods for equality constraints and for inequality constraints, active set method.
3. Constrained minimization methods. Reduction to unconstrained minimization: penalty function and barrier function. SQP-method.
4. Linear multi-criterial programming. Pareto-optimal solution. Optimal solution with respect to a meta-criterion.
5. Convex nondifferentiable minimization. Fejer monotonicity. Optimality conditions. Subgradient projection method.

Teaching methods

Traditional lecture, classes with exercises, laboratory with application of appropriate software.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

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 classes grade (30%), the lab’s grade (30%) and the examination’s grade (40%)

Recommended reading

1. A. Cegielski, Podstawy optymalizacji, skrypt do wykładu
2. W. Findeisen, J. Szymanowski, A. Wierzbicki, Teoria i metody obliczeniowe optymalizacji, PWN, Warszawa, 1980.
3. Z. Galas, I. Nykowski (red.), Zbiór zadań z programowania matematycznego, część I, II, PWN, Warszawa, 1986, 1988.
4. W. Grabowski, Programowanie matematyczne, PWE, Warszawa, 1980.
5. A. Cegielski, Programowanie matematyczne - część 1 - Programowanie liniowe, Uniwersytet Zielonogórski, Zielona Góra, 2002.
6. Badania operacyjne (red. W. Sikora),  PWE, Warszawa, 2008.

Further reading

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. M. Brdyś, A. Ruszczyński, Metody optymalizacji w zadaniach, WNT, Warszawa, 1985.
6. J. Stadnicki, Teoria i praktyka rozwiązywania zadań optymalizacji, WNT, Warszawa, 2006.

Notes

Modified by dr Robert Dylewski, prof. UZ (last modification: 20-09-2019 11:49)