Non-linear Optimalization - P413006
Title: Optimalizace nelineárních problémů
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2024
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Level:  
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Kubíček Milan prof. RNDr. CSc.
Isoz Martin Ing. Ph.D.
Classification: Mathematics > Mathematics General
Is interchangeable with: AP413006
Examination dates   
Annotation -
Extreme values of functions of several real variables. Extreme with equality and inequality constrainst. Linear programming. Nonlinear programming, direct search methods, gradient methods, Newton method. Methods for constrained extreme. Elements of dynamic programming. Vector optimization, Pareto set construction.
Last update: Kubíček Milan (02.10.2018)
Aim of the course -

Students will be able to: Understand and formulate an optimization problems. Solve the problem in simple cases, use the appropriate software in more complex cases. Classify the problem and propose an efficient solution. Solve the given project.

Last update: Kubíček Milan (02.10.2018)
Course completion requirements -

Solving the given problem. Written and oral exam.

Last update: Kubíček Milan (02.10.2018)
Literature -

Kubíček M.: Optimalizace inženýrských procesů. SNTL Praha 1986.

Edgar T. F., Himmelblau D. M.,Lasdon L. S.: Optimization of Chemical Processes, McGraw-Hill, Boston, 2001.

L. T. Biegler: New directions for nonlinear process optimization. Current Opinion in Chemical Engineering, vol. 21, pp. 32–40, 2018.

Further literature individually.

Last update: Borská Lucie (06.09.2019)
Teaching methods -

Self-study, consultation, solution of given problem.

Last update: Kubíček Milan (02.10.2018)
Syllabus -

1. Formulation of the optimization problem.

2. Extrems of functions of real variables - methods of classical analysis.

3. Extrems of functions of real variables - unconstrained extreme, extrem with equality constraints.

4. Extrems of real variable functions - Extrems with inequality constraints.

5. Linear programming.

6. Simplex method.

7. Non-linear programming.

8. Adaptive search methods.

9. Gradient methods.

10. Penalty functions.

11. Fundamentals of dynamic programming.

12. Resource distribution problem.

13. Fundamentals of vector optimization.

14. Construction of a Pareto set.

Last update: Kubíček Milan (02.10.2018)
Entry requirements -

Mathematics A, B

Last update: Borská Lucie (16.09.2019)
Registration requirements -

none

Last update: Borská Lucie (16.09.2019)