TÜRKÇE
ENGLISH
Information
| Code | ISB222 |
| Name | Optimization Techniques - II |
| Term | 2024-2025 Academic Year |
| Semester | 4. 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 |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NİMET ÖZBAY |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to comprehend unconstrained and constrained multivariate optimization problems and their solution methods and to gain the ability to solve some nonlinear optimization problems
Course Content
The content of this course consists of the following topics: Unconstrained Univariate Optimization, Unconstrained Bivariate Optimization, Unconstrained Multivariate Optimization, Multivariate Optimization with Equality Constraints, Jacobian Method, Lagrangian Method, Inequality Restricted Optimization, Kuhn-Tucker Conditions, Nonlinear Optimization Techniques
Course Precondition
None
Resources
-Optimizasyon Teknikleri, Hasan Bal, Gazi Üniversitesi, Ankara, 1995. -A First Course in Optimization Theory, Rangarajan K. Sundaram, Cambridge University Press, 1996. -Optimizasyon, Ayşen Apaydın, A.Ü., Ankara, 2005. -Doğrusal Programlama, İmdat Kara, Bilim Teknik Yayınevi, 1991. -Yöneylem Araştırması, Hamdy A. Taha, Literatür Yayıncılık, 2003. -Optimizasyon ve Matlab Uygulamaları, Aysun Tezel Özturan, Nobel Akademik Yayıncılık, 2022.
Notes
-Optimizasyon, Ayşen Apaydın, A.Ü., Ankara, 2005.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Uses unconstrained optimization problems and solution methods |
| LO02 | Uses the solution methods of unconstrained multivariate optimization problems |
| LO03 | Solves equality constrained multivariate optimization problems |
| LO04 | Has the ability to apply Jacobian and Lagrangian methods |
| LO05 | Solves inequality constrained optimization problems |
| LO06 | Writes the Kuhn-Tucker conditions |
| LO07 | Explains some nonlinear optimization methods and their relationships |
| LO08 | Solves some nonlinear optimization problems |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | 3 |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 2 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | 2 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Unconstrained Univariate Optimization, | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 2 | Unconstrained Bivariate Optimization | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Unconstrained Multivariate Optimization | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Multivariate Optimization with Equality Constraints | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 5 | Jacobian Method | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Lagrangian Method | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Equality Constrained Multivariate Optimization Problems | Source reading | Öğretim Yöntemleri: Problem Çözme |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Sensitivity Analysis in Equality Constrained Multivariate Optimization | Source reading | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Elimination methods | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Exhaustive Search, Dichotomous Search | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Fibonacci Search | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Golden Ratio Search | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Gradient Descent | Source reading | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Problem Solving | Source reading | Öğretim Yöntemleri: Problem Çözme |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | 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 | ||