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

EEE 514 | Course Introduction and Application Information

Course Name

Optimization Methods and Applications

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
EEE 514	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	Prof. Dr. Aydın AKAN
Course Lecturer(s)	Prof. Dr. Aydın AKAN
Assistant(s)	-

Course Objectives

The aim of this course is to introduce iterative solutions to optimization problems encountered in engineering. Topics include vector spaces, projection theorem, orthogonal functions and least squares approach, unconstrained optimization, gradient methods, constrained optimization, linear and nonlinear optimization. All methods discussed in the course will be reinforced by homeworks and MATLAB applications.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	explain the basic optimization problem,
2	apply iterative methods for unconstrained optimization,
3	define analytical and iterative solutions of equality constrained optimization,
4	explain linear programming methods,
5	analyze nonlinear optimization problems.

Course Description

In this course, various analytic and iterative optimization methods will be introduced to determine the "best" or "most desired" solution to the problems encountered in Engineering. The most commonly used optimization methods will be presented with computer solutions to problems in electrical engineering. Programs will be developed for iterative solution of optimization methods using MATLAB platform.

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	Linear spaces, normed linear spaces. Projection theorem. Orthogonal functions and least squares approximation.	Chap 7. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
2	Differential geometry, directional derivatives, Necessary and sufficient conditions for local and global minima.	Chap 7. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
3	Unconstrained optimization problem, Analytical and iterative solution. The steepest descent method.	Chap 8. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
4	Step size parameter search methods for steepest descent algorithm: Constant, variable, polynomial fit, Fibonacci and Golden section searches.	Chap 8. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
5	Newton-Raphson iterative method, Conjugate directions method	Chap 9-10. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
6	Conjugate gradient (Fletcher-Reeves) and Variable metric (Fletcher-Powell-Davidon) methods	Chap 9. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
7	Equality constrained optimization, analytical solution, Lagrange multiplier method.	Chap 11. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
8	Midterm Exam
9	Iterative solutions to equality constrained optimization, steepest descent, Newton Raphson, and penalty methods.	Chap 12-13. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
10	Inequality constrained optimization. Linear programming. Fundamental theorem of linear programming.	Chap 2. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
11	Simplex method.	Chap 3. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
12	Applied nonlinear programming	Chap 14. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
13	Kuhn-Tucker theorem and its applications	Chap 14. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
14	Quadratic programming. Rosen's gradient projection method. Bellman's Optimality Principle.	Chap 15. Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4th Ed., Springer, 2016. ISBN: 9783319188423
15	Review of the course
16	Final Exam

Course Notes/Textbooks	Luenberger, David.G., Ye, Yinyu, Linear and Nonlinear Programming, 4^th Ed., Springer, 2016. ISBN: 9783319188423
Suggested Readings/Materials	Nash, S.G., Sofer A., Linear and Nonlinear Programming, Mc Graw Hill, 1996. ISBN: 9780070460652

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	30
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	2	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
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	7	10	70
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	20	20
Final Exam	1	30	30
		Total	210

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.		-	-	-	-	-