TÜRKÇE
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Information
| Code | EKMS305 |
| Name | Optimization |
| Term | 2024-2025 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SÜLEYMAN BİLGİN KILIÇ |
| Course Instructor |
Arş.Gör.Dr. Salih ÇAM
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To give analytical thinking and problem-solving skills to the students by means of learning and application of the optimization methods
Course Content
Introduction to the theory of optimization, necessary and sufficient conditions for the global maximum or minimum of unrestricted functions, Newton-Raphson method, constrained optimization of continuous functions, lagrangian method in the form of equality constraints, linear programming and the simplex method, sensitivity analysis, expansion of the Lagrangian method in the form inequality constraints, determination of the Kuhn-Tucker necessary and sufficient conditions for the non-linear constrained problems, non-linear programming algorithms; gradient descent method, quadratic programming, geometric programming and stochastic programming
Course Precondition
No prerequisites
Resources
Öztürk, A. (1984). Yöneylem araştırması. Uludağ Üniversitesi. Winston, W. L. (1991). Operations research: applications and algorithms. Taha, H. A., & Taha, H. A. (1997). Operations research: an introduction (Vol. 7). Upper Saddle River, NJ: Prentice hall.
Notes
related statistical and econometric packages
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Solves the problems via analytical thinking |
| LO02 | Constructs the mathematical models |
| LO03 | Knows basic concepts related to optimization |
| LO04 | Transforms problems have complex structure into mathematical problems. |
| LO05 | Finds effective solutions to problems |
| LO06 | Solves mathematical functions with appropriate algorithms |
| LO07 | Expresses problems mathematically. |
| LO08 | Finds solutions to problems with related algorithms. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and theorems in the fields of Econometrics, Statistics and Operations research | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires basic Mathematics, Statistics and Operation Research concepts | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Describes the necessary concepts of Business | 4 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Equipped with the foundations of Economics, and develops Economic models | 5 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | 3 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Analyzes/interprets at the conceptual level to develop solutions to problems | 4 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Collects/analyses data from reliable data sources for the purpose of study | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Interprets the results analyzed with the model | 4 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Combines the information obtained from different sources within the framework of academic rules in a field of research | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Adapts traditional approaches, practices and methods to a new study when necessary | 2 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Uses a package program of Econometrics, Statistics, and Operation Research | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | In addition to herself/himself professional development, constantly improves in scientific, cultural, artistic and social fields in line with interests and abilities | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in its field. | |
| PLO15 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses Turkish and at least one other foreign language, academically and in the business context | |
| PLO16 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | |
| PLO17 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on current economic and social issues | |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to the theory of optimization | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 2 | Necessary and sufficient conditions for the global maximum or minimum of unrestricted functions | reading the related topic | Öğretim Yöntemleri: Anlatım |
| 3 | Newton-Raphson method | reading the related topic | Öğretim Yöntemleri: Soru-Cevap |
| 4 | Constrained optimization of continuous functions | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 5 | Lagrangian method in the form of equality constraints | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 6 | Linear programming and the simplex method | reading the related topic | Öğretim Yöntemleri: Alıştırma ve Uygulama |
| 7 | The sensitivity analysis | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | making preparations by examining the relevant topics from the weekly program | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Expansion of the Lagrangian method in the form inequality constraints | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 10 | Determination of the Kuhn-Tucker necessary and sufficient conditions for the non-linear constrained problems | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 11 | Non-linear programming algorithms | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 12 | Gradient descent method | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 13 | Quadratic programming | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım |
| 14 | Geometric programming | making preparations by examining the relevant topics from the weekly program | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Stochastic programming | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Alıştırma ve Uygulama |
| 16 | Term Exams | students take term exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | students take term exams | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||