APPLIED MATHEMATICS (TURKISH, NON-THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
EEE5010 | Optimization | Fall Spring |
3 | 0 | 3 | 9 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | En |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Prof. Dr. SÜREYYA AKYÜZ |
Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ |
Course Objectives: | To equip students with the mathematical theory of optimization and solution methods. |
The students who have succeeded in this course; Students will - be able to formulate optimization problems - understand basic differences between various constraints - apply numerical techniques to solve optimization problems |
Optimization as a decision making problem. Optimization over an open set. Optimization under equality constraints; Lagrange multipliers. Optimization under inequality constraints. Linear programming. Numerical methods. |
Week | Subject | Related Preparation | |
1) | The Optimization Problem. Examples. | ||
2) | Mathematical preliminaries | ||
3) | Mathematical preliminaries | ||
4) | The Weierstrass Theorem. Application to example problems. | ||
5) | Optimization over an open set. Necessary and sufficient conditions. | ||
6) | Numerical techniques: Gradient algorithm, Newton's method. | ||
8) | Optimization with equality constraints. Lagrange multipliers. | ||
9) | Optimization with inequality constraints. Kuhn-Tucker conditions. | ||
10) | Linear programming: Standard maximization and minimization problems. | ||
11) | Linear programming: Primal and dual problems. Duality theorem. Optimality conditions. | ||
12) | The Simplex algorithm. | ||
13) | Discrete dynamic programming. | ||
14) | Large optimization problems. Decomposition methods. |
Course Notes: | 1. P. Varaia, Lecture Notes on Optimization, web |
References: | 1. C.T. Kelley, Iterative Methods for Optimization, SIAM |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | 5 | % 25 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 1 | % 25 |
Preliminary Jury | % 0 | |
Final | 1 | % 50 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Workload | |
Course Hours | 14 | 42 | |
Laboratory | |||
Application | |||
Special Course Internship (Work Placement) | |||
Field Work | |||
Study Hours Out of Class | 16 | 136 | |
Presentations / Seminar | |||
Project | |||
Homework Assignments | 5 | 10 | |
Quizzes | |||
Preliminary Jury | |||
Midterms | 1 | 2 | |
Paper Submission | |||
Jury | |||
Final | 1 | 2 | |
Total Workload | 192 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | |
4) | Ability to make individual and team work on issues related to working and social life. | |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | |
6) | Ability to use mathematical knowledge in technology. | |
7) | To apply mathematical principles to real world problems. | |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | |
10) | To apply mathematical principles to real world problems. | |
11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |