ACADEMICS
Course Details
ELE704 - Optimization
2024-2025 Fall term information
The course is not open this term
ELE704 - Optimization
| Program | Theoretıcal hours | Practical hours | Local credit | ECTS credit |
| PhD | 3 | 0 | 3 | 10 |
| Obligation | : | Elective |
| Prerequisite courses | : | - |
| Concurrent courses | : | - |
| Delivery modes | : | Face-to-Face |
| Learning and teaching strategies | : | Lecture, Question and Answer, Problem Solving |
| Course objective | : | It is aimed to give the following topics to the students; a) Recognising and classifying an optimisation problem, b) Tools for learning and analysing convex sets and functions, c) Basic algorithms used in solving convex optimisation problems, d) Duality concept in constrained problems and the techniques being used to apply them, mainly staying in the context of convex optimisation, so that they can solve problems which they may encounter with in their studies/projects. |
| Learning outcomes | : | Recognise and classify optimisation problems Model the problem s/he encounters with as an optimisation problem Know which algorithms can s/he use to solve the problem s/he established, know the advantages and disadvantages of these algorithms Apply the techniques and algorithms s/he learnt in the class to her/his thesis studies and also real-life applications Have the adequate knowledge to follow and understand advanced up-to-date optimisation algorithms |
| Course content | : | Brief reminder of linear algebra topics, Convexity, convex sets and functions, Gradiant Descent, Steepest Descent, Newton Algorithms and their variations for unconstrained problems, Constrained problems and Karush-Kuhn-Tucker Conditions, Modification of the above algorithms for unconstrained problems to constrained problems, İnterior Point Algorithms (Penalty ve Barrier Methods) |
| References | : | 1. Luenberger, Linear and Nonlinear Programming, Kluwer, 2002.; 2. Boyd and Vandenberghe, Convex Optimization, Cambridge, 2004.; 3. Baldick, Applied Optimization, Cambridge, 2006.; 4. Freund, Lecture Notes, MIT.; 5. Bertsekas, Lecture Notes, MIT.; 6. Bertsekas, Nonlinear Programming, Athena Scientific, 1999. |
| Weeks | Topics |
|---|---|
| 1 | Brief reminder of linear algebra topics |
| 2 | Brief reminder of linear algebra topics |
| 3 | Optimality conditions for unconstrained problems Convex Sets |
| 4 | Convex and concave functions Conditions for convexity Operations that preserve convexity |
| 5 | Quadratic functions, forms and optimization Optimality conditions Unconstrained minimization |
| 6 | Descent Methods Convergence |
| 7 | Algorithms: Gradient Descent Algorithm |
| 8 | Algorithms: Steepest Descent Algorithm |
| 9 | Algorithms: Newton?s Algorithm |
| 10 | Midterm Exam |
| 11 | Constrained optimization Duality |
| 12 | Optimality conditions, KKT Conditions Algorithms: Feasible Direction Method, Active Set Method |
| 13 | Algorithms: Gradient Projection Method, Newton?s Algorithm with Equality Constraints |
| 14 | Algorithms: Penalty and Barrier Methods |
| 15 | Study week |
| 16 | Final Exam |
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 13 | 30 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Quiz | 0 | 0 |
| Midterms | 1 | 30 |
| Final exam | 1 | 40 |
| Total | 100 | |
| Percentage of semester activities contributing grade success | 60 | |
| Percentage of final exam contributing grade success | 40 | |
| Total | 100 | |
| Course activities | Number | Duration (hours) | Total workload |
|---|---|---|---|
| Course Duration | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, etc.) | 14 | 3 | 42 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 13 | 5 | 65 |
| Quiz | 0 | 0 | 0 |
| Midterms (Study duration) | 1 | 25 | 25 |
| Final Exam (Study duration) | 1 | 30 | 30 |
| Total workload | 43 | 66 | 204 |
| Key learning outcomes | Contribution level | |||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1. | Has highest level of knowledge in certain areas of Electrical and Electronics Engineering. | |||||
| 2. | Has knowledge, skills and and competence to develop novel approaches in science and technology. | |||||
| 3. | Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research. | |||||
| 4. | Can independently carry out all stages of a novel research project. | |||||
| 5. | Designs, plans and manages novel research projects; can lead multidisiplinary projects. | |||||
| 6. | Contributes to the science and technology literature. | |||||
| 7. | Can present his/her ideas and works in written and oral forms effectively; in Turkish or English. | |||||
| 8. | Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them. | |||||
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest