Course Details

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
1ECE602MATHEMATICAL OPTIMIZATION: THEORY AND METHODS3+0+037,513.05.2025

 
Course Details
Language of Instruction English
Level of Course Unit Doctorate's Degree
Department / Program ELECTRICAL AND COMPUTER ENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course Develop a comprehensive understanding of the fundamentals of mathematical optimization, including least-squares, linear programming, and convex and nonlinear optimization techniques.
Analyze convex sets, convex functions, operations that preserve convexity, and their properties including separating and supporting hyperplanes, and generalized inequalities.
Formulate various optimization problems, including convex, linear, quadratic, and geometric programming problems.
Solve convex optimization problems involving generalized inequality constraints by applying descent methods.
lems.
Course Content This course provides an in-depth exploration of advanced optimization techniques, with a focus on both convex and nonlinear optimization. The course begins with a review of foundational mathematical optimization concepts, including least-squares, linear programming, and convex analysis. Students will delve into the theory of convex sets, convex functions, and their properties, gaining insight into operations that preserve convexity and the application of generalized inequalities. The second half of the course focuses on convex optimization problems and unconstrained minimization methods. Topics such as linear and quadratic optimization, geometric programming, and descent methods (including gradient descent, steepest descent, and Newton’s method) will be covered in detail. Students will also explore practical implementation strategies for solving complex optimization problems.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Ali Hakan TOR
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Stephen, B. O. Y. D., & Vandenberghe, L. (2022). Convex optimization. Cambridge university press.


Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıyıl İçi Çalışmalarının Başarı Notunun Katkısı 4 % 30
Ödev 4 % 40
Proje/Çizim 1 % 30
Total
9
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Ev Ödevi 4 10 40
Sınıf İçi Aktivitesi 14 1 14
Teslim İçin Hazırlık 4 5 20
Ders dışı çalışma 7 5 35
Yüz Yüze Ders 14 3 42
Derse Devam 14 3 42
Total Work Load   Number of ECTS Credits 7,5 193

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Analyze affine and convex sets, operations that preserve convexity in mathematical models, and concepts such as separating hyperplanes, and generalized inequalities.
2 Interpret the properties of convex functions, including conjugate, quasiconvex.
3 Formulate real-world optimization problems involving linear, quadratic, and geometric programming challenges.
4 Critique unconstrained minimization techniques such as gradient descent, steepest descent, and Newton's method.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Mathematical optimization
2 Least-squares and linear programming
3 Convex optimization, Nonlinear optimization
4 Affine and convex sets, Some important examples
5 Generalized in equalities Separating and supporting hyperplanes
6 Convex functions, Basic properties and examples
7 Quasiconvex functions
8 Convex optimization problems, Linear optimization problems
9 Quadratic optimization problems, Generalized inequality constraints
10 Unconstrained minimization problems
11 Descent methods, Gradient descent method
12 Steepest descent method
13 Newton’s method
14 Quasi-Newton Method

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
C1 2 4 4 3 3 2 3 1 2 1 1
C2 2 4 4 3 3 2 3 1 2 1 1
C3 2 4 4 3 3 2 3 1 2 1 1
C4 5 3 4 3 3 4 4 1 4 1 4

  Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant

  
  https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=77586&lang=en
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