470-8742/02 – 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 A
Year3Semesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation
Intended for the facultiesUSP, FSIntended 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:

D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont 1999. ISBN 1-886529-00-0. M. S: Bazaraa, C. M. Shetty, Nonlinear programming, J. Wiley, New York 1979. 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. ISBN 1-85233-028-7.

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, simulated annealing, tabu search. 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: 2015/2016 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  15
        Examination Examination 70  21 3
Mandatory attendence participation: Obligatory participation in 80% of the 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 yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B0588A170003) Applied Sciences and Technologies MTM P Czech Ostrava 3 Choice-compulsory type A study plan
2023/2024 (B0588A170003) Applied Sciences and Technologies CHE P Czech Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170003) Applied Sciences and Technologies FYZ P Czech Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170003) Applied Sciences and Technologies MAR P Czech Ostrava 3 Choice-compulsory type B study plan
2023/2024 (B0588A170003) Applied Sciences and Technologies MTR P Czech Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies MTM P Czech Ostrava 3 Choice-compulsory type A study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies CHE P Czech Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies FYZ P Czech Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies MAR P Czech Ostrava 3 Choice-compulsory type B study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies MTR P Czech Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies MTM P Czech Ostrava 3 Choice-compulsory type A study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies CHE P Czech Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies FYZ P Czech Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies MAR P Czech Ostrava 3 Choice-compulsory type B study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies MTR P Czech Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies MTM P Czech Ostrava 3 Choice-compulsory type A study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies CHE P Czech Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies FYZ P Czech Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies MAR P Czech Ostrava 3 Choice-compulsory type B study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies MTR P Czech Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies MTM P Czech Ostrava 3 Choice-compulsory type A study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies CHE P Czech Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies FYZ P Czech Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies MAR P Czech Ostrava 3 Choice-compulsory type B study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies MTR P Czech Ostrava 3 Choice-compulsory type B study plan
2018/2019 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 3 Choice-compulsory study plan
2017/2018 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 3 Choice-compulsory study plan
2016/2017 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 3 Choice-compulsory study plan
2015/2016 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 3 Choice-compulsory study plan

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