Syllabus ( IE 515 )
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Basic information
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| Course title: |
Mathematical Programming |
| Course code: |
IE 515 |
| Lecturer: |
Assist. Prof. Kemal Dinçer DİNGEÇ
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| ECTS credits: |
7.5 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
1/2, Fall |
| Level of course: |
Second Cycle (Master's) |
| Type of course: |
Area Elective
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| Language of instruction: |
Turkish
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
none |
| Professional practice: |
No |
| Purpose of the course: |
This course aims to teach the following topics: Fermat rule, Lagrange multipliers, duality theory, Karush-Kuhn-Tucker conditions, convexity, conic optimization, linear optimization, networks, integer programming. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Construct continuous optimization models and identify their main optimality conditions
Contribution to Program Outcomes
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Increase his/her knowledge level about Operations Research, Management Sciences and Production Management.
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Develop solutions that yield optimal outputs by using limited resources efficiently
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Become an authority in modeling, simulation, process management and related subjects.
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Acquire scientific knowledge
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Work effectively in multi-disciplinary research teams
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Find out new methods to improve his/her knowledge.
Method of assessment
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Written exam
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Homework assignment
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Solve optimization problems using optimality conditions and existence results.
Contribution to Program Outcomes
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Increase his/her knowledge level about Operations Research, Management Sciences and Production Management.
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Develop solutions that yield optimal outputs by using limited resources efficiently
-
Become an authority in modeling, simulation, process management and related subjects.
-
Acquire scientific knowledge
-
Find out new methods to improve his/her knowledge.
Method of assessment
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Written exam
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Homework assignment
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Apply the duality theory for linear and nonlinear optimization problems.
Contribution to Program Outcomes
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Increase his/her knowledge level about Operations Research, Management Sciences and Production Management.
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Develop solutions that yield optimal outputs by using limited resources efficiently
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Propose alternative point of views by analyzing complex industrial problems methodically
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Become an authority in modeling, simulation, process management and related subjects.
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Acquire scientific knowledge
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Find out new methods to improve his/her knowledge.
Method of assessment
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Written exam
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Homework assignment
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Learn modelling techniques and solution methods for optimization problems with integer variables.
Contribution to Program Outcomes
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Increase his/her knowledge level about Operations Research, Management Sciences and Production Management.
-
Develop solutions that yield optimal outputs by using limited resources efficiently
-
Propose alternative point of views by analyzing complex industrial problems methodically
-
Become an authority in modeling, simulation, process management and related subjects.
-
Acquire scientific knowledge
-
Find out new methods to improve his/her knowledge.
Method of assessment
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Written exam
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Homework assignment
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Contents
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| Week 1: |
Univariate Unconstrained Optimization |
| Week 2: |
Multivariate Unconstrained Optimization |
| Week 3: |
Multivariate Equality Constrained Optimization. Homework. |
| Week 4: |
Multivariate Inequality Constrained Optimization |
| Week 5: |
Gradient Methods. Homework. |
| Week 6: |
Duality Theory |
| Week 7: |
Midterm exam |
| Week 8: |
Linear Optimization. Homework. |
| Week 9: |
Quadratic Optimization |
| Week 10: |
Graph Optimization. Homework. |
| Week 11: |
Economic and Engineering Applications |
| Week 12: |
Integer Optimization. Homework. |
| Week 13: |
Conic Optimization |
| Week 14: |
Applications of Conic Optimization |
| Week 15*: |
- |
| Week 16*: |
Final exam |
| Textbooks and materials: |
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| Recommended readings: |
Optimization: Insights and Applications, Brinkhuis and Tikhomirov, 2005, Princeton Univ. Press
Convex Optimization, Boyd and Vandenberghe, 2003, Cambridge Univ. Press |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
7 |
30 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
3,5,8,10,12 |
30 |
| Quiz: |
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0 |
| Final exam: |
16 |
40 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
7 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
3 |
5 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
7 |
1 |
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| Mid-term: |
2 |
1 |
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| Personal studies for final exam: |
4 |
4 |
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| Final exam: |
3 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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