1. SylabUZ
2. Wydział Nauk Ścisłych i Przyrodniczych
3. semestr zimowy 2022/2023
4. Mathematics - drugiego stopnia z tyt. magistra
5. Mathematical Programming

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Mathematical Programming - opis przedmiotu

Cel przedmiotu

Students learn methods for solving constrained optimization problems, in particular linear programming and quadratic programming problems. They will learn the basics of multi-criteria optimization and non-differentiable minimization. In addition, they will become familiar with the appropriate software.

Wymagania wstępne

Zapisz zmiany

Linear Algebra 1 and 2, Calculus 1 and 2, Fundamentals of Optimization.

Zakres tematyczny

Linear programming. A linear programming (ZPL) task and tasks that can be reduced to ZPL. Graphical method. Simplex algorithm, phase I and II. Duality and dual simplex algorithm.

Quadratic programming. Methods used for equality and inequality constraints, active constraints method.

Constrained minimization methods. Reduction to minimization without constraints: penalty function and barrier function. SQP method.

Multi-criteria linear programming. Multi-criteria linear programming task. Pareto-optimal solutions. Optimal solutions due to the meta-criterion.

Non-differentiable convex minimization. Problems in non-differentiable minimization. Monotonicity in Fejer's sense. Optimality conditions. Subgradient projection method.

Metody kształcenia

Traditional lecture; auditorium exercises in which students solve tasks; a laboratory in which students become familiar with software used to solve mathematical programming tasks

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Exercises: checking the level of students' preparation and their activity during classes; colloquium with tasks of varying difficulty, allowing you to assess whether the student has achieved the learning outcomes.

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

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

The final grade for the course takes into account the grade for exercises (30%), laboratory (30%) and exam grade (40%).

The condition for passing the course is positive grades from exercises, laboratory and exam.

Literatura podstawowa

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

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 28-02-2024 15:46)