Course: Numerical Methods of Optimization

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Course title Numerical Methods of Optimization
Course code KMF/INNMO
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Karamazov Simeon, prof. Ing. Dr.
  • Rak Josef, RNDr. Ph.D.
Course content
Optimization in applications and examples. Minimalization of one variable functions and numerical methods. Minimalization of multivariable functions. Nondifferenciable optimization. Minimalization of quadratic functions. Gradient methods. Newton and QuasiNewton methods. Optimization with and without constraints. Lagrange function and Kuhn_Tucker conditions. Quadratic programming. Nonlinear programming.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Projection, Skills training
Learning outcomes
The aim of the course is introduction to optimization and numerical methods in the sphere of mathematical programming. Methods used in technical computing will be described. Matlab software is used for practical examples.
Expansion of analytical and logical cogitation. Higher level of mathematical knowledge. Summary of optimalization methods and their functions in computation problems. Active solving of practical optimalization problems.
Prerequisites
Knowledge of mathematics in the range of university basic courses. Knowledge of numerical methods in the range of KIT/INAM course. Basic knowledge of programming.

Assessment methods and criteria
Oral examination, Written examination, Home assignment evaluation, Creative work analysis, Didactic test, Discussion

The credit is granted upon completion of following conditions: active participation in seminars (labs); completion of all given tasks; passing all written tests. The examination comprises of three parts practical exercises, writing tests and a theoretical (speaking) test; at least 51 % success rate in each part is required.
Recommended literature
  • Francis Scheid Schaum's Outline of Numerical Analysis.
  • J. Nocedal and S.J. Wright. Numerical Optimization.
  • Mišík. Funkcionální analýza. Bratislava: Alfa, 1988.
  • Nožička et al.Theorie der linearen Optimierung, Berlin, Akademieverlag 1972. Theorie der linearen Optimierung. Berlin: Akademieverlag, 1972.
  • Seifart, Manteufel. Lineare Optimierung. Leipzig, 1985.
  • Schwarz. Matematické metody ve fyzice. Praha: SNTL, 1972.
  • Sirovich. Introduction to Applied Mathematics. Berlin: Springer, 1988.
  • Taylor. Úvod do funkcionální analýzy. Praha: Academia, 1973.
  • Won Y. Yang, Wenwu Cao. Applied Numerical Methods Using MATLAB.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Information Technology (2015) Category: Informatics courses - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Communication and Controlling Technology (2016) Category: Electrical engineering, telecommunication and IT - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Communication and Controlling Technology (2014) Category: Electrical engineering, telecommunication and IT - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Information Technology (2016) Category: Informatics courses - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Process Control (2014) Category: Special and interdisciplinary fields - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Process Control (2013) Category: Special and interdisciplinary fields - Recommended year of study:-, Recommended semester: -
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Communication and Controlling Technology (2015) Category: Electrical engineering, telecommunication and IT - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Process Control (2015) Category: Special and interdisciplinary fields - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Process Control (2016) Category: Special and interdisciplinary fields - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Electrical Engineering and Informatics Study plan (Version): Information Technology (2014) Category: Informatics courses - Recommended year of study:-, Recommended semester: Summer