470-4503/01 – Methods of Optimization (MO)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. Petr Beremlijski, Ph.D.Subject version guarantordoc. Ing. Petr Beremlijski, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
DOS35 prof. RNDr. Zdeněk Dostál, DSc.
SAD015 Ing. Marie Sadowská, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

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, ruský překlad Mir Moskva 1982. 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. Z. Dostal, Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities Springer, New York 2009. ISBN: 0387848053, ISBN-13: 9780387848051

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

There are not defined other requirements for 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

Part-time form (validity from: 2011/2012 Winter semester, validity until: 2021/2022 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation 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:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS K Czech Ostrava 2 Compulsory study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS P Czech Ostrava 2 Compulsory study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS P Czech Ostrava 2 Compulsory study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS K Czech Ostrava 2 Compulsory study plan
2020/2021 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2020/2021 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS K Czech Ostrava 2 Compulsory study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS P Czech Ostrava 2 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS P Czech Ostrava 2 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics NMS K Czech Ostrava 2 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2020/2021 Summer
2019/2020 Winter
2013/2014 Winter