|
Lecturer(s)
|
-
Ženčák Pavel, RNDr. Ph.D.
-
Machalová Jitka, doc. RNDr. Ph.D., MBA
-
Burkotová Jana, Mgr. Ph.D.
|
|
Course content
|
1. Constrained optimization, its applications, examples, introductory definitions and basic conceptions. 2. Necessary an sufficient optimality conditions. Constraint qualifications. 3. Lagrangian function. Lagrangian dual problems. 4. Complementarity problems. Lemke's method. 5. Quadratic programming with equality and inequality constraints. Active set method. 6. Methods for nonlinear programming problems with linear constraints - null-space method and gradient projection method. 7. Penalty methods for general nonlinear programming. 8. Principles of sequential quadratic programming method. Concept of interior-point methods.
|
|
Learning activities and teaching methods
|
|
unspecified
|
|
Learning outcomes
|
Gain knowledge about theory and algorithms required to solve optimization problems with constraints.
Knowledge Gain useful knowledge about theory and algorithms in order to study and solve optimization problems with constraints.
|
|
Prerequisites
|
Student has to pass the basic course Optimization methods. Standard knowledge from mathematical analysis and linear algebra. Elemental experience with computation on PC.
|
|
Assessment methods and criteria
|
unspecified
Credit: the student has to compute given examples. Exam: the student has to understand the subject and be acquainted with theoretical and practical aspects of the methods.
|
|
Recommended literature
|
-
Bierlaire, M. (2015). Optimization: Principles and Algorithms. EPFL Press.
-
D.G. Luenberger, Y. Ye. (2008). Linear And Nonlinear Programming. 3rd Edition.
-
Dostál, Z., Beremlijski, P. (2018). Metody optimalizace. Ostrava.
-
J. Nocedal, S. J. Wright. (2006). Numerical Optimization. Springer.
-
M. J. Kochenderfer, T. A. Wheeler. (2019). Algorithms for Optimization. Cambridge, MIT Press.
-
Machalová, J., Netuka, H. (2013). Nelineární programování: Teorie a metody. Olomouc.
-
M.S. Bazaraa, H.D. Sherali, C.M. Shetty. (2006). Nonlinear Programming. Theory And Algorithms.
-
O. Došlý. (2005). Základy konvexní analýzy a optimalizace v R^n. Brno.
|