457-0008/01 – Methods of Optimization (MOP)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. RNDr. Zdeněk Dostál, DSc.Subject version guarantorprof. RNDr. Zdeněk Dostál, DSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year4Semesterwinter
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesMaster
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

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.

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

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. 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: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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