SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Non-linear Optimalization - P413006
Title: Optimalizace nelineárních problémů
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type: doctoral
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.
Interchangeability : D413007
Is interchangeable with: AP413006
Annotation -
Last update: Kubíček Milan prof. RNDr. CSc. (02.10.2018)
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.
Aim of the course -
Last update: Kubíček Milan prof. RNDr. CSc. (02.10.2018)

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.

Literature -
Last update: Borská Lucie RNDr. Ph.D. (06.09.2019)

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.

Teaching methods -
Last update: Kubíček Milan prof. RNDr. CSc. (02.10.2018)

Self-study, consultation, solution of given problem.

Syllabus -
Last update: Kubíček Milan prof. RNDr. CSc. (02.10.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

Mathematics A, B

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

none

Course completion requirements -
Last update: Kubíček Milan prof. RNDr. CSc. (02.10.2018)

Solving the given problem. Written and oral exam.

Coursework assessment
Form Significance
Defense of an individual project 20
Examination test 40
Oral examination 40

 
VŠCHT Praha