M.SC. in Electrical and Electronics Engineering (With Thesis)

EEE 515 | Course Introduction and Application Information

Course Name

Introduction to Convex Optimization

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
EEE 515	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second / Third Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	Dr. Öğr. Üyesi Pınar Oğuz Ekim
Course Lecturer(s)	Dr. Öğr. Üyesi Pınar Oğuz Ekim
Assistant(s)	-

Course Objectives

This course aims to teach the tools and train the students to recognize convex optimization problems that arise in scientific and engineering applications. Besides, it aims to present the basic theory, and concentrate on modeling aspects and results that are useful in applications.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	Determine the convex sets, cones and functions
2	Formulate convex optimization problems
3	Determine the dual problems
4	Develop skills to solve common problems in
5	Implement convex optimization problems and methods in MATLAB based on a given algorithmic description or theory

Course Description

Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Related Preparation	Learning Outcome
1	Introduction to mathematical optimization; least-squares and linear programming; convex optimization; course goals and topics.	CH1, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 052183378
2	Overview of linear algebra	Linear Algebra and its Applications, Gill Strang, Cengage Learning ISBN-10: 0534422004
3	Convex sets and cones.	CH2, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
4	Common and important examples; operations that preserve convexity.	CH2, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
5	Convex functions	CH3, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
6	Common examples; operations that preserve convexity; quasiconvex and log-convex functions.	CH3, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
7	Convex optimization problems, linear and quadratic programs;	CH4, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
8	Second-order cone and semidefinite programs; quasiconvex optimization problems;	CH4, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
9	Duality, Lagrange dual function and problem	CH5, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
10	Optimality conditions	CH5, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
11	Applications: approximation and fitting; Norm approximation; regularization; robust optimization	CH6, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
12	Applications: statistical estimation; Maximum likelihood and MAP estimation; detector design.	CH7, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
13	Applications: geometric problems; Projection; extremal volume ellipsoids; placement and location problems.	CH8, Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787
14	Presentation of term projects to class
15	Presentation of term projects to class
16	Presentation of term projects to class

Course Notes/Textbooks	Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, ISBN-10: 0521833787 Numerical Optimization, J. Nocedal and S. Wright, Springer Series in Operations Research, ISBN-13: 978-0-387-22742-9 Linear Algebra and its Applications, Gill Strang, Cengage Learning ISBN-10: 0534422004
Suggested Readings/Materials	Lectures on Modern Convex Optimization, A. Ben-Tal and A. Nemirovski, MPS-SIAM Series on Optimization, ISBN-10: 0898714915 Nonlinear Programming, D. Bertsekas, Athena Scientific, ISBN-10: 1886529000

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
Participation	1	10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	50
Presentation / Jury
Project	1	40
Seminar / Workshop
Oral Exams
Midterm
Final Exam
Total

Weighting of Semester Activities on the Final Grade	3	100
Weighting of End-of-Semester Activities on the Final Grade
Total

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	6	10	60
Presentation / Jury			0
Project	1	75	75
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam			0
		Total	225

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information		-	-	-	X	-
2	Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations		-	-	X	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines		-	-	X	-	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	X	-	-
5	Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	X	-	-
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	X	-	-	-
7	Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process.		-	-	-	-	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility.		-	-	-	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	-	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	-	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Electrical and Electronics Engineering applications, knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications.		-	-	-	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics.		-	-	-	-	-