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

Gurantor department	Department of Applied Mathematics	Credits	4
Subject guarantor	prof. RNDr. Zdeněk Dostál, DSc.	Subject version guarantor	prof. RNDr. Zdeněk Dostál, DSc.
Study level	undergraduate or graduate	Requirement	Choice-compulsory
Year	2	Semester	winter
		Study language	Czech
Year of introduction	1992/1993	Year of cancellation	2009/2010
Intended for the faculties	FEI	Intended for study types	Master

Extent of instruction for forms of study
Form of study	Way 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

Other requirements

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 name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (145)	51	3
Examination	Examination	100	0	3
Exercises evaluation	Credit	45	0	3

Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Form	Study language	Tut. centre	Year	Type of duty
2007/2008	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2007/2008	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2007/2008	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2007/2008	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2007/2008	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics		P	Czech	Ostrava	2	Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2006/2007	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics		P	Czech	Ostrava	2	Choice-compulsory	study plan
2005/2006	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials		P	Czech	Ostrava	4	Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2005/2006	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics		P	Czech	Ostrava	2	Choice-compulsory	study plan
2004/2005	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials		P	Czech	Ostrava	4	Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	5	Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2004/2005	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics		P	Czech	Ostrava	2	Choice-compulsory	study plan
2003/2004	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials		P	Czech	Ostrava	4	Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	5	Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2003/2004	(B2612) Electrical Engineering and Computer Science	(1801R001) Computer Science		P	Czech	Ostrava	5	Choice-compulsory	study plan
2002/2003	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials		P	Czech	Ostrava	4	Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	4	Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava		Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava	3	Choice-compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	4	Choice-compulsory	study plan
2000/2001	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava	3	Choice-compulsory	study plan
2000/2001	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	4	Choice-compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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