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Course, academic year 2023/2024
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Numerical Optimization Methods - NMNV534
Title: Numerické metody optimalizace
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Petr Tichý, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NMNV503, NNUM121
Interchangeability : NMNV503, NNUM121
Is interchangeable with: NNUM121
In complex interchangeability with: NMNV503
In complex incompatibility with: NMNV503
Annotation -
Last update: T_KNM (07.04.2015)
Optimization and minimization techniques. Optimization method, global convergence, speed of convergence. Minimization of a functional, descent techniques, nonlinear conjugate gradient method, Quasi-Newton methods, trust-region methods. Least-squares problems, the Gauss-Newton method. Theory of constrained optimization, Lagrange multipliers, convex optimization, penalty and barrier methods, projection and dual methods. The course is suitable for students focused on industrial mathematics and numerical analysis.
Course completion requirements -
Last update: doc. RNDr. Petr Tichý, Ph.D. (23.04.2020)

It is not necessary to obtain a course-credit before passing the exam.

The course-credit will be granted for a presentation of results of numerical experiments.

There are two additional attempts to obtain the course-credit.

Literature -
Last update: doc. RNDr. Petr Tichý, Ph.D. (23.04.2020)

J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM 1996, originally published in 1983.

R. Fletcher, Practical Methods of Optimization, 2nd edition Wiley 1987, (republished 2000).

D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, Third edition. Springer, New York, MA, 2008.

J. Nocedal and S. Wright, Numerical Optimization, Second edition, Springer Verlag 2006.

W. Sun and Y-X. Yuan, Optimization theory and methods. Nonlinear programming. Springer Optimization and Its Applications, 1. Springer, New York, 2006.

Requirements to the exam -
Last update: doc. RNDr. Petr Tichý, Ph.D. (16.02.2018)

The exam is oral. Requirements for the oral exam correspond to the syllabus of the course, presented at the lectures.

Syllabus -
Last update: doc. RNDr. Petr Tichý, Ph.D. (23.04.2020)

Theory of unconstrained optimization (necessary and sufficient conditions, the role of convexity, classification of convergence), minimization in a given direction (Golden section search, curve fitting, Newton), inexact line search (Goldstein, Armijo, and Wolfe conditions), basic descent methods (the method of steepest descent and the Newton method), conjugate direction methods (the nonlinear conjugate gradient method), Quasi-Newton methods (the quasi-Newton condition, rank-one update, DFP, BFGS, the Broyden family), trust-region methods, least-squares problems (the Gauss-Newton and the Levenberg-Marquart method). Theory of constrained optimization (Lagrange multipliers, necessary and sufficient conditions).

Entry requirements -
Last update: doc. RNDr. Petr Tichý, Ph.D. (02.05.2018)

Fundamentals of multivariable calculus and numerical linear algebra. Basic knowledge of the Matlab programming language.

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