470-8742/06 – Methods of Optimization (MONT)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Ing. Petr Beremlijski, Ph.D.Subject version guarantordoc. Ing. Petr Beremlijski, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory type B
Year3Semesterwinter
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials

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.

Compulsory literature:

J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2006. R. Fletcher: Practical Methods of Optimization, John Wiley & Sons, Chichester 1997.

Recommended literature:

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.

Way of continuous check of knowledge in the course of semester

Verification of study: Written exam (max 10 marks). Project (max 20 marks) Conditions for credit: Minimum 10 marks on tests and project.

E-learning

Other requirements

No additional requirements are imposed on a student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70 (70) 21 3
                Písemná zkouška Written examination 50  1
                Ústní zkouška Oral examination 20  0
Mandatory attendence participation: At least 80% attendance on exercises.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2024/2025 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2024/2025 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2024/2025 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2024/2025 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2023/2024 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2022/2023 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MM P English Ostrava 3 Choice-compulsory type A study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies CH P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies F P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MR P English Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MT P English Ostrava 3 Choice-compulsory type B study plan

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