470-8742/02 – Methods of Optimization (MONT)

Gurantor department	Department of Applied Mathematics	Credits	4
Subject guarantor	doc. Ing. Petr Beremlijski, Ph.D.	Subject version guarantor	doc. Ing. Petr Beremlijski, Ph.D.
Study level	undergraduate or graduate	Requirement	Choice-compulsory type B
Year	3	Semester	winter
		Study language	Czech
Year of introduction	2015/2016	Year of cancellation
Intended for the faculties	USP, FS	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
BER95	doc. Ing. Petr Beremlijski, Ph.D.
DOS35	prof. RNDr. Zdeněk Dostál, DSc.

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

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:

BERTSEKAS, Dimitri P. Nonlinear Programming. 3rd edition. Athena Scientific, 2016. ISBN 978-1886529052.

Recommended literature:

NOCEDAL, Jorge a Stephen WRIGHT. Numerical Optimization. 2nd edition. Springer, 2006. ISBN 978-0387303031.

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

No additional requirements are imposed on a 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. 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

Full-time form (validity from: 2015/2016 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit and Examination	Credit and Examination	100 (100)	51
Credit	Credit	30	15
Examination	Examination	70	21	3

Mandatory attendence participation: Obligatory participation in 80% of the exercises.

Show history

Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

Show history

Occurrence in study plans

Academic year	Programme	Branch/spec.	Zaměření	Form	Study language	Tut. centre	Year	Type of duty
2024/2025	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2024/2025	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2024/2025	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2024/2025	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2024/2025	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2023/2024	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2023/2024	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2023/2024	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2023/2024	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2023/2024	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2022/2023	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2022/2023	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2022/2023	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2022/2023	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2022/2023	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2021/2022	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2021/2022	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2021/2022	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2021/2022	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2021/2022	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2020/2021	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2020/2021	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2020/2021	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2020/2021	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2020/2021	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2019/2020	(B0588A170003) Applied Sciences and Technologies		MTM	P	Czech	Ostrava	3	Choice-compulsory type A	study plan
2019/2020	(B0588A170003) Applied Sciences and Technologies		CHE	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2019/2020	(B0588A170003) Applied Sciences and Technologies		FYZ	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2019/2020	(B0588A170003) Applied Sciences and Technologies		MAR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2019/2020	(B0588A170003) Applied Sciences and Technologies		MTR	P	Czech	Ostrava	3	Choice-compulsory type B	study plan
2018/2019	(B3968) Applied Sciences and Technologies	(3901R076) Applied Sciences and Technologies		P	Czech	Ostrava	3	Choice-compulsory	study plan
2017/2018	(B3968) Applied Sciences and Technologies	(3901R076) Applied Sciences and Technologies		P	Czech	Ostrava	3	Choice-compulsory	study plan
2016/2017	(B3968) Applied Sciences and Technologies	(3901R076) Applied Sciences and Technologies		P	Czech	Ostrava	3	Choice-compulsory	study plan
2015/2016	(B3968) Applied Sciences and Technologies	(3901R076) Applied Sciences and Technologies		P	Czech	Ostrava	3	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

Předmět neobsahuje žádné hodnocení.