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Methods of Optimization

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-8742/01
Number of ECTS Credits Allocated3 ECTS credits
Type of Course Unit *Choice-compulsory type B
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
DOS35prof. RNDr. Zdeněk Dostál, DSc.
BER95doc. Ing. Petr Beremlijski, Ph.D.
Summary
Optimization methods are basic tools for improving design and technology. The students will learn about basic optimization problems, conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for the soluving engineering problems.
Learning Outcomes of the Course Unit
The student will be able to recognize basic classes of optimization problems and will understand conditions of their solvability and correct formulation. Effective algorithms, heuristics and software will be presented in an extent that is useful for solving engineering problems, so that the student will be able to apply their knowledge to the solution of practical problems.
Course Contents
Lectures:
Unconstrained minimization. One-dimensional minimization of unimodular functions.
Conditions of minimum, the Newton method and its modification. Gradient methods.
Constrained minimization. Karush-Kuhn-Tucker conditions of optimality.
Penalization methods for constrained minimization.
Duality in convex programming. Saddle points, Uzawa algorithm and augmented Lagrangians.
Non-smooth optimization, subgradients and optimality conditions.
Global optimization, genetic and evolutionary algorithms.
Software.

Exercises:
Introduction to the MATLAB programming.
Implementation of the golden section and Fibonacci series methods.
Implemenation of the Newton-like methods.
Implementation of the gradient based method.
Implementation of the penalty methody for equality constrained minimization.
Implementation of the augmented Lagrangian metod.
Implementation of algorithms for global optimization.
Solution of selected engeneering problems using optimization software.
Recommended or Required Reading
Required Reading:
J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006.

R. Fletcher: Practical Methods of Optimization, John Wiley & Sons, Chichester 1997.
Dostál, Z., Beremlijski, P.: Metody optimalizace, Text vytvořený při realizaci projektu Matematika pro inženýry 21. století, 2012.

D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont 1999.

J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006.
Recommended Reading:
D. T. Pham and D. Karaboga, Intelligent Optimization Techniques, Springer, London 2000.

Z. Dostal, Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities Springer, New York 2009.
R. Fletcher: Practical Methods of Optimization, John Wiley & Sons, Chichester 1997.

D. T. Pham and D. Karaboga, Intelligent Optimization Techniques, Springer, London 2000.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit30 15
        ExaminationExamination70 21