Faculty Of Engıneerıng
Industrıal Engıneerıng (Englısh)
Course Information
| OPTIMIZATION METHODS | |||||
|---|---|---|---|---|---|
| Code | Semester | Theoretical | Practice | National Credit | ECTS Credit |
| Hour / Week | |||||
| INE409 | Fall | 3 | 0 | 3 | 4 |
| Prerequisites and co-requisites | |
|---|---|
| Language of instruction | English |
| Type | Elective |
| Level of Course | Bachelor's |
| Lecturer | Asst. Prof. Dr. Türker ERTEM |
| Mode of Delivery | Face to Face |
| Suggested Subject | |
| Professional practise ( internship ) | None |
| Objectives of the Course | To build up the mathematical models. To show application areas in real-life. To apply the solution algorithms. |
| Contents of the Course | Introduction and basic concepts. Unconstrained optimization. Analytic solution, Numerical methods and algorithms in unconstrained optimization. Constrained Optimization: Optimization with equality constraints, Optimization with equality and inequality constraints, Optimization with special constraints. Linear programming and applications. |
Learning Outcomes of Course
| # | Learning Outcomes |
|---|---|
| 1 | Produce to solutions about engineering problems |
| 2 | Give information about optimization sciences |
| 3 | Produce to solutions about optimization scienes problems |
| 4 | Give information about last technologies of optimization sciences |
Course Syllabus
| # | Subjects | Teaching Methods and Technics |
|---|---|---|
| 1 | Mathematical Review I. Methods of Proof and Some Notation II. Vector Spaces and Matrices III. Transformations | |
| 2 | IV. Concepts from Geometry V. Elements of Calculus | lecturing, discussing, problem solving |
| 3 | Unconstrained Optimization VI. Basics of Set-Constrained and Unconstrained Optimization 6.1 Introduction 6.2 Conditions for Local Minimizers | lecturing, discussing, problem solving |
| 4 | VII. One-Dimensional Search Methods 7.1 Golden Section Search 7.2 Fibonacci Search | lecturing, discussing, problem solving |
| 5 | 7.3 Newton's Method 7.4 Secant Method | lecturing, discussing, problem solving |
| 6 | Nonlinear Constrained Optimization XIX. Problems with Equality Constraints 19.1 Introduction 19.2 Problem Formulation | lecturing, discussing, problem solving |
| 7 | 19.3 Tangent and Normal Spaces 19.4 Lagrange Condition | lecturing, discussing, problem solving |
| 8 | 19.5 Second-Order Conditions 19.6 Minimizing Quadratics Subject to Linear Constraints | lecturing, discussing, problem solving |
| 9 | XXI. Convex Optimization Problems 21.1 Introduction 21.2 Convex Functions 21.3 Convex Optimization Problems | lecturing, discussing, problem solving |
| 10 | Linear Programming XV. Introduction to Linear Programming 15.1 A Brief History of Linear Programming 15.2 Simple Examples of Linear Programs 15.3 Two-Dimensional Linear Programs | lecturing, discussing, problem solving |
| 11 | 15.4 Convex Polyhedra and Linear Programming 15.5 Standard Form Linear Programs 15.6 Basic Solutions | lecturing, discussing, problem solving |
| 12 | 15.7 Properties of Basic Solutions 15.8 A Geometric View of Linear Programs | lecturing, discussing, problem solving |
| 13 | XVII. Duality 17.1 Dual Linear Programs 17.2 Properties of Dual Problems | lecturing, discussing, problem solving |
| 14 | XVI. Simplex Method 16.1 Solving Linear Equations Using Row Operations 16.2 The Canonical Augmented Matrix | lecturing, discussing, problem solving |
| 15 | ||
| 16 | Final Exam |
Course Syllabus
| # | Material / Resources | Information About Resources | Reference / Recommended Resources |
|---|---|---|---|
| 1 | Chong E.K.P., Żak S.H. An Introduction to Optimization, Second Edition Wiley (2001) | ||
| 2 | Griva I., Nash, S.G., Sofer A. Linear and Nonlinear Optimization, Second Edition SIAM (2009) | ||
| 3 | Luenberger D.G., Ye Y. Linear and Nonlinear Programming, Third Edition Springer (2008) |
Method of Assessment
| # | Weight | Work Type | Work Title |
|---|---|---|---|
| 1 | 30% | Mid-Term Exam | Mid-Term Exam |
| 2 | 30% | Mid-Term Exam | Mid-Term Exam |
| 3 | 40% | Final Exam | Final Exam |
Relationship between Learning Outcomes of Course and Program Outcomes
| # | Learning Outcomes | Program Outcomes | Method of Assessment |
|---|---|---|---|
| 1 | Produce to solutions about engineering problems | 1͵4͵11 | 1͵2͵3 |
| 2 | Give information about optimization sciences | 1͵4͵11 | 1͵2͵3 |
| 3 | Produce to solutions about optimization scienes problems | 1͵4͵11 | 1͵2͵3 |
| 4 | Give information about last technologies of optimization sciences | 1͵4͵11 | 1͵2͵3 |
Work Load Details
| # | Type of Work | Quantity | Time (Hour) | Work Load |
|---|---|---|---|---|
| 1 | Course Duration | 14 | 3 | 42 |
| 2 | Course Duration Except Class (Preliminary Study, Enhancement) | 14 | 1 | 14 |
| 3 | Presentation and Seminar Preparation | 0 | 0 | 0 |
| 4 | Web Research, Library and Archival Work | 0 | 0 | 0 |
| 5 | Document/Information Listing | 0 | 0 | 0 |
| 6 | Workshop | 0 | 0 | 0 |
| 7 | Preparation for Midterm Exam | 2 | 6 | 12 |
| 8 | Midterm Exam | 2 | 2 | 4 |
| 9 | Quiz | 0 | 0 | 0 |
| 10 | Homework | 0 | 0 | 0 |
| 11 | Midterm Project | 0 | 0 | 0 |
| 12 | Midterm Exercise | 0 | 0 | 0 |
| 13 | Final Project | 0 | 0 | 0 |
| 14 | Final Exercise | 0 | 0 | 0 |
| 15 | Preparation for Final Exam | 1 | 16 | 16 |
| 16 | Final Exam | 1 | 2 | 2 |
| 90 | ||||