470-4503/02 – Methods of Optimization (MO)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2015/2016Year 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.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined 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 on unconstrained optimization (45 minutes, max 10 marks). Written exam on constrained optimization (45 minutes, max 10 marks). Conditions for credit: At least 25 marks on progress assessment and projects.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

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. Implementation of the feasible direction method (SLP). Implementation of the active set method for bound constrained quadratic programming. Implementation of the augmented Lagrangian metod. Implementation of algorithms for global optimization. Solution of selected engeneering problems using optimization software. Projects: Comparing performance of the methods for unconstrained optimization using a numerical example (max 10 marks). Comparing performance of the methods for constrained optimization using a numerical example (max 10 marks). Solution of a selected engineering problem (max 10 marks). Computer labs: 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. Implementation of the feasible direction method (SLP). Implementation of the active set method for bound constrained quadratic programming. 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 points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history
Combined form (validity from: 2015/2016 Winter 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  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 2 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 2 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 2 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 2 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 2 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 2 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 2 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 2 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 2 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner