| Course Type | Elective Course |
|---|
| Course Level | Master's Degree With Thesis |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 10 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Explain the elements of linear algebra and multivariate calculus
- Solve systems of equations
- Define the convex analysis and its applications to optimisation of multivariate functions
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | Special topics in differential and integral calculations. Vector spaces. Matrices and determinants. Analytical and numerical methods for solving equation systems. Quadratic forms. Convex combination and convex sets. Convex and concave functions. Local and global optima in multi variate functions. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Linear Algebra and Real Analysis |
|
2nd Week |
The linear space - Vectors and Matrices - Systems of Equations - Quadratic Forms |
|
3rd Week |
Convex Sets and Functions - Convex and Affine Hulls |
|
4th Week |
Relative Interior, Closure, and Continuity - Recession Cones |
|
5th Week |
Convexity and Optimization -- Global and Local Minima |
|
6th Week |
The Projection Theorem - The separation Theorem, Saddle Point and Minimax Theory |
|
7th Week |
Subgradients and Constrained Optimization -- Directional Derivatives |
|
8th Week |
Midterm |
|
9th Week |
Subgradients and Subdifferentials -- Directional Derivative of the Max Function |
|
10th Week |
Optimality Conditions |
|
11th Week |
Introduction to Lagrange Multipliers |
|
12th Week |
Informative Lagrange Multipliers - Sensitivity -- Alternative Lagrange Multipliers |
|
13th Week |
Lagrangian Duality |
|
14th Week |
Conjugate Duality |
|
| Recommended or Required Reading | Dimitri P. Bertsekas (2003), Convex Analysis and Optimization, Athena Scientific (ISBN-10: 1886529450); (2) Stephen Boyd and Lieven Vandenberghe (2004), Convex Optimization, Cambridge University Press (ISBN-10: 0521833787). |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Problem Solving
- Practice
- Presentation
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Project |
1 |
30 |
| Total(%) |
|
60 |
| Contribution of In-term Studies to Overall Grade(%) |
|
60 |
| Contribution of Final Examination to Overall Grade(%) |
|
40 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
|
|
|
| Individual or group work |
14 |
14 |
196 |
| Preparation for Final exam |
1 |
25 |
25 |
| Course hours |
14 |
3 |
42 |
| Preparation for Midterm exam |
1 |
25 |
25 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
1 |
14 |
14 |
| Total Work Load | 306 |
| Total Work Load / 30 (h) | 10.2 |
| ECTS Credit of the Course | 10 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
