470-8742/03 – Methods of Optimization (MONT)

Gurantor departmentDepartment of Applied MathematicsCredits3
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesUSPIntended for study typesFollow-up Master
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+1

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



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.

Way of continuous check of knowledge in the course of semester

Verification of study: Written exam on unconstrained optimization (45 minutes, max 15 marks). Written exam on constrained optimization (45 minutes, max 15 marks). Conditions for credit: At least 15 marks on progress assessment.


Other requirements

Additional requirements for students are not.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Lectures: An introduction to the calculus of variations. Linear spaces, funkcionls and their differentials (Fréchet, Gateaux). Euler equation and the solution of the classical problems of variational calculus. Unconstrained minimization. One-dimensional minimization of unimodular functions. Conditions of minimum, the Newton method and its modification. Gradient methods, method of conjugate gradients. Constrained minimization. Karush-Kuhn-Tucker conditions of optimality. Penalization and barrier methods for constrained minimization. Feasible direction method (SLP) and active set strategy for bound constrained problems. Duality in convex programming. Saddle points, Uzawa algorithm and augmented Lagrangians. Linear programming, simplex method. 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 conjugate gradient method. Implementation of the penalty methody for equality constrained minimization.

Conditions for subject completion

Full-time form (validity from: 2017/2018 Winter semester, validity until: 2020/2021 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  35
Mandatory attendence parzicipation: Written and oral exam

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava 1 Choice-compulsory study plan
2018/2019 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava 1 Choice-compulsory study plan
2017/2018 (N3942) Nanotechnology (3942T001) Nanotechnology P English Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner