MU:MU24006 Optimization Methods in Pract. - Course Information
MU24006 Optimization Methods in PracticeMathematical Institute in Opava
- Extent and Intensity
- 2/1/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Mathematics (programme MU, N1101)
- Course objectives
- 1. Introduction: Modeling and optimization. Types of problems and methods, examples. Assignment of semester projects. 2. Extrema of functions of one varriable. Fibonacci method and golden section search. Secant method. Newton's method. 3. Optimization without constraints: gradient methods, Newton's method and its variants, the method of the conjugate gradient, quasi-Newton methods, comparative methods. 4. Optimization with constraints: Nonconvex and convex problems, method of Lagrange multipliers and generaliizations, penalization and barrier methods, method of projection and reduction of the gradient. 5. Linear, quadratic, and nonlinear programming. Linear problems with special structure. Duality. 6. Further practical methods: Stochastic methods, genetic algorithms, discrete methods.
- Extremal problems.
Lagrange multipliers, the Kuhn-Tucker theorem.
Classical variational calculus.
The instruments of the theory of extremal problems.
The Lagrange principle for smooth bounded problems.
- Extremal problems.
- recommended literature
- J. W. Chinneck. Practical Optimization: A Gentle Introduction. URL info
- Topics in Applied Math: Methods of Optimization. URL info
- V. M. Alexejev, S. V. Fomin, V. M. Tichomirov. Matematická teorie optimálních procesů. Academia, Praha, 1991. ISBN 80-200-0319-3. info
- P. E. Gill, W. Murray, M. H. Wright. Practical optimalization. Academic Press, London and New York, 1981. info
- Language of instruction
- Further Comments
- The course can also be completed outside the examination period.