Infopaket

Decomposing methods of discrete optimization

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

2

Know the history of the formation and development of discrete optimization; basic concepts of discrete optimization. Know modern development trends, scientific and applied achievements of discrete optimization. Know modern approaches, optimization methods, computer technologies and tools for solving current scientific problems of discrete optimization. Know the theoretical methods of studying the complexity and speed of computational algorithms. To be able to formulate the general methodological basis of own scientific research from new research positions, to realize its urgency, the purpose and value for development of discrete optimization. Be able to develop and apply methods of discrete optimization for mathematical modeling and optimization of scientific and technical, economic, environmental and social processes and systems.

Full-time form

1. Know: the material of standard university courses in mathematical analysis, linear algebra, operations research and decision theory, probability theory, graph theory, discrete optimization using modern computing resources; program in one of the current programming languages. 2. Be able to: develop, analyze and apply decomposition algorithms to solve problems and applied problems, implement algorithms to program in one of the modern programming languages.

The discipline "Problems of cryptography, optimization and risk analysis" belongs to the list of disciplines of choice by blocks. The subject of module 2 "Decomposition methods of discrete optimization" of the discipline are current problems of discrete optimization, relating to the basic principles of development of mathematical methods of decomposition to solve complex problems of discrete optimization. It provides acquaintance, deepening and improvement of knowledge, which is an element of fundamental mathematical training of students, and which can be used in the practical application of models and methods of discrete optimization in solving complex problems of optimal design, management of economic and technical facilities and systems. as well as in the implementation of research projects. Taught in the 7th semester, 30 hours. (2 ECTS credit), of which seminars - 16 hours, independent work - 14 hours. There are 2 substantive parts and a test.

1. Sergienko IV Mathematical models and methods for solving discrete optimization problems. Kiev: Nauk. opinion, 1988. 472 p. 2. Sergienko IV Informatics in Ukraine: formation, development of the problem. K .: Nauk. opinion, 1999. 354 p. 3. Sergienko IV, Shilo VP Discrete optimization problems. Problems, methods of solution, research. Kiev: Nauk. opinion, 2003. 263 p. 4. Corte B., Figen J. Combinatorial optimization. Theory and algorithms. M .: Izd-vo MCNMO, 2015. 720 s. 5. Pisaruk NN Models and methods of mixed-integer programming. Minsk: Belarusian State University, 2008. 250 p. 6. Lesdon L.S. Optimization of large systems. M .: Nauka, 1975. 430 s. 7. Semenova NV, Kolechkina LM Vector problems of discrete optimization on combinatorial sets: research methods and solutions. Kyiv: Nauk. opinion, 2009. 266 p.

Lecture, individual work

Current assessment, control work, credit

Ukrainian