Methods of optimization

Description: Acquaintance with basic mathematical models and the development of numerical methods for solving classical extreme tasks, as well as familiarity with modern areas of development of optimization methods. In general, the course material is focused on the ability to properly classify a specific applied task, choose the most suitable solution method and implement it in the form of an algorithm and program.

Amount of credits: 6

Пререквизиты:

• Ordinary differential equation

Course Workload:

Component: Component by selection

Cycle: Profiling disciplines

Goal

• To instill in the student knowledge and skills in the compilation of mathematical models of practical extreme problems, the use of methods for solving them and the software implementation of these methods.

Objective

• Master methods and techniques for solving optimization problems;

Learning outcome: knowledge and understanding

• Know the basics of optimization theory

Learning outcome: applying knowledge and understanding

• Be able to apply optimization methods in solving applied problems

Learning outcome: formation of judgments

• Be able to analyze the results

Learning outcome: communicative abilities

• Be able to work in a team

Learning outcome: learning skills or learning abilities

• Improve those who have knowledge

Teaching methods

When conducting training sessions, the use of the following educational technologies is envisaged: - Information and communication technology; - Technology for the development of critical thinking; - Design technology; - Technology of integrated learning; - Technologies of level differentiation; - Group technologies; - Traditional technologies (lectures, laboratory classes)

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Введение в оптимизацию
• Линейное программирование
• Элементы выпуклого анализа
• Методы минимизации функций
• Принцип максимума Понтрягина
• Динамическое программирование

Key reading

• Карманов В. Г. Математическое программирование: Учеб. пособие. — 5-е изд., стереотип. — М., 2014. — 264 с.
• Лемешко, Б.Ю. Методы оптимизации: Конспект лекций / Б.Ю. Лемешко. – Новосибирск: Изд-во НГТУ, 2019. – 126 с.
• Методы оптимизации: учебник и практикум для бакалавриата и магистратуры/Ф.П. Васильев и др. - М.: Издательство Юрайт, 2019. - 375 с.
• Струченков В.И. Методы оптимизации в прикладных задачах. - М.: СОЛОН-ПРЕСС, 2012. - 320 с.

Further reading

• Вентцель Е.С. Исследование операций: задачи, принципы, методология. –М.: Дрофа, 2014. – 208 с.