Fundamentals of Convex Optimization with Applications

Објавено: June 28, 2022
1. Course Title Fundamentals of Convex Optimization with Applications
2. Code 4ФЕИТ08З012
3. Study program NULL
4. Organizer of the study program (unit, institute, department) Faculty of Electrical Engineering and Information Technologies
5. Degree (first, second, third cycle) First cycle
6. Academic year/semester 7. Number of ECTS credits 6
8. Lecturer D-r Katerina Hadji-Velkova Saneva, D-r Zoran Hadji-Velkov
9. Course Prerequisites Passed: Mathematics 1, Mathematics 2
10. Course Goals (acquired competencies): Introduction to the basic theory of convex optimization. Understanding and interpreting the basic concepts and tools of convex analysis and their application in mathematical optimization. Recognition and formalization of engineering problems as models for mathematical optimization. Solving convex optimization problems that appear in engineering.
11. Course Syllabus: Concept of mathematical optimization. Importance of convex optimization in electrical engineering and information technologies (examples). Convexity versus non-convexity. Convex functions. Convex sets. Unconstrained optimization. Linear programming. Lagrange multiplier method. Application of numerical methods for solving optimization problems. Gradient descent methods. Quadratic optimization. Least squares problem. Convex programming. Optimality conditions. Karush-Kuhn-Tucker conditions. Dual problem. Interior point method. Software tools for optimization. Machine learning for optimization. Modeling and solving optimization problems in electrical engineering and information technologies.
12. Learning methods: Classic lectures supported by solving practical exercises and computation problems, homeworks.
13. Total number of course hours 3 + 2 + 0 + 0
14. Distribution of course hours 180
15. Forms of teaching 15.1. Lectures-theoretical teaching 45
15.2. Exercises (laboratory, practice classes), seminars, teamwork 30
16. Other course activities 16.1. Projects, seminar papers 35
16.2. Individual tasks 20
16.3. Homework and self-learning 50
17. Grading 17.1. Exams 0
17.2. Seminar work/project (presentation: written and oral) 40
17.3. Activity and participation 10
17.4. Final exam 50
18. Grading criteria (points) up to 50 points 5 (five) (F)
from 51to 60 points 6 (six) (E)
from 61to 70 points 7 (seven) (D)
from 71to 80 points 8 (eight) (C)
from 81to 90 points 9 (nine) (B)
from 91to 100 points 10 (ten) (A)
19. Conditions for acquiring teacher’s signature and for taking final exam Аttend classes regularly
20. Forms of assessment During the semester, two partial written exams are foreseen (at the middle and at the end of the semester). For students who have passed the partial exams, a final oral exam can be conducted. The final grade includes the points from the partial exams, the points from the individual student work (homeworks), and the final oral exam.
Students who take one written exam instead of two partial exams can take it in the scheduled exam sessions. For the student who has passed the written exam, a final oral exam can be conducted. The final grade includes the points from the written exam, the points from the individual student work (homeworks), and the final oral exam.
21. Language Macedonian and English
22. Method of monitoring of teaching quality Internal evaluation and surveys
23. Literature
23.1. Required Literature
No. Author Title Publisher Year
1 S. Slobec, J. Petric Nelinearno programiranje Naucna knjiga 1989
2 D.G. Luenberger и Y. Ye Linear and Nonlinear Programming (fourth ed.) Springer, Cham 2016
3 S. Boyd и L. Vandenberghe Convex optimization Cambridge university press 2004