GRADUATE SCHOOL
M.SC. in Electrical and Electronics Engineering (Without Thesis)
EEE 514 | Course Introduction and Application Information
| Course Name |
Optimization Methods and Applications
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|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 514
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
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| Course Language |
English
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| Course Type |
Elective
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| Course Level |
Second / Third Cycle
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| 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 |
The students who succeeded in this course;
|
| 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. |
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Core Courses | |
| Major Area Courses |
X
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| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 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 |
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| Suggested Readings/Materials |
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EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| 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
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
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 modelling, analyses and resolves the complex problems that arise in this process. |
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| 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. |
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| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. |
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| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
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| 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. |
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| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest