|
Lecturer(s)
|
-
Machalová Jitka, doc. RNDr. Ph.D., MBA
-
Burkotová Jana, Mgr. Ph.D.
-
Radová Jana, Mgr.
-
Machalová Monika, Ing.
-
Škorňa Stanislav, Mgr.
|
|
Course content
|
1. Unconstrained optimization - subject, applications, examples. Introductory definitions and basic conceptions. 2. Necessary and sufficient optimality conditions. 3. Univariate minimization. Minimization without using derivatives (comparative method, Fibonacci search method, golden section search method). Methods using derivatives (bisection, Newton method). 4. Derivative-free minimization of functions of several variables. Nelder-Mead method. Hooke-Jeeves method. 5. Minimization of quadratic functions using gradient methods. 6. Descent methods. Fundamental principles. Line search methods. Convergence analysis. 7. Method of steepest descent and conjugate gradient method for nonquadratic function. 8. Newton's method and its modifications. 9. Quasi-Newton methods. 10. Solution of systems of nonlinear equations. Multivariate minimization and its connection with nonlinear algebraic equations. 11. Constrained optimization, its importance for applications, examples. Introductory definitions and basic conceptions. First-order necessary optimality conditions. Karush-Kuhn-Tucker conditions. Geometric interpretation of KKT conditions. 12. Quadratic programming and its importance. Methods for solution of problems with equality constraints.
|
|
Learning activities and teaching methods
|
|
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
|
|
Learning outcomes
|
Gain knowledge about theory and algorithms required to solve unconstrained optimization problems and quadratic programming.
Knowledge Gain useful knowledge about theory and algorithms in order to study and solve unconstrained optimization problems and quadratic programming.
|
|
Prerequisites
|
Standard knowledge from mathematical analysis, linear algebra and numerical methods.
KMA/MA1 and KMA/MA2 and KAG/LA1A and KMA/ZNUM
|
|
Assessment methods and criteria
|
Oral exam, Seminar Work
Active participation. Credit: the student has to make a seminary work Exam: the student has to understand the subject and be acquainted with theoretical and practical aspects of the methods.
|
|
Recommended literature
|
-
J. E. Dennis, R. B. Schnabel. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall Englewood Cliffs N. J..
-
J. Machalová, H. Netuka. (2013). Nelineární programování: Teorie a metody. Olomouc.
-
J. Machalová, H. Netuka. (2013). Numerické metody nepodmíněné optimalizace. Olomouc.
-
J. Nocedal, S. J. Wright. (2006). Numerical Optimization. Springer.
-
L. Lukšan. (2011). Numerické optimalizační metody. Nepodmíněná minimalizace. Technical report no. 1152. Praha.
-
M. S. Bazaraa, H. D. Sherali, C. M. Shetty. (2006). Nonlinear Programming. Theory And Algorithms.
-
S. Míka. (1997). Matematická optimalizace. FAV ZČU, Plzeň.
-
Z. Dostál, P. Beremlijski. (2012). Metody optimalizace. Ostrava.
|