ECTS - Introduction to Optimization
Introduction to Optimization (MATH490) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Introduction to Optimization | MATH490 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | To give a basic knowledge of optimization in mathematics, provide an introduction to the applications, theory, and algorithms of linear and nonlinear optimization |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Fundamentals of optimization, representation of linear constraints, linear programming, Simplex method, duality and sensitivity, basics of unconstrained optimization, optimality conditions for constrained problems. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | I. Basics Chapter 1. Optimization Models 1.1. Introduction 1.3. Linear Equations 1.4. Linear Optimization | Related sections in Ref. [1] |
| 2 | 1.5. Least-Squares Data Fitting 1.6. Nonlinear Optimization 1.7. Optimization Applications | Related sections in Ref. [1] |
| 3 | Chapter 2. Fundamentals of Optimization 2.1. Introduction 2.2. Feasibility and Optimality 2.3. Convexity 2.4. The General Optimization Algorithm | Related sections in Ref. [1] |
| 4 | 2.5. Rates of Convergence 2.6. Taylor Series 2.7. Newton’s Method for Nonlinear Equations and Termination | Related sections in Ref. [1] |
| 5 | Chapter 3. Representation of Linear Constraints 3.1. Basic Concepts 3.2. Null and Range Spaces | Related sections in Ref. [1] |
| 6 | II Linear Programming Chapter 4. Geometry of Linear Programming 4.1. Introduction 4.2. Standard Form 4.3. Basic Solutions and Extreme Points | Related sections in Ref. [1] |
| 7 | Chapter 5. The Simplex Method 5.1. Introduction 5.2. The Simplex Method | Related sections in Ref. [1] |
| 8 | Chapter 6. Duality and Sensitivity 6.1. The Dual Problem 6.2. Duality Theory | Related sections in Ref. [1] |
| 9 | III Unconstrained Optimization Chapter 11. Basics of Unconstrained Optimization 11.1. Introduction 11.2. Optimality Conditions 11.3. Newton’s Method for Minimization | Related sections in Ref. [1] |
| 10 | 11.4. Guaranteeing Descent 11.5. Guaranteeing Convergence: Line Search Methods | Related sections in Ref. [1] |
| 11 | IV Nonlinear Optimization Chapter 14. Optimality Conditions for Constrained Problems 14.1. Introduction 14.2. Optimality Conditions for Linear Equality Constraints | Related sections in Ref. [1] |
| 12 | 14.3. The Lagrange Multipliers and the Lagrangian Function 14.4. Optimality Conditions for Linear Inequality Constraints | Related sections in Ref. [1] |
| 13 | 14.5. Optimality Conditions for Nonlinear Constraints | Related sections in Ref. [1] |
| 14 | Review | |
| 15 | Review | |
| 16 | Final |
Sources
| Course Book | 1. Igor Griva, Stephen G. Nash, Ariela Sofer, Linear and Nonlinear Optimization Second Edition, SIAM, 2009 |
|---|---|
| 2. Edwin K.P. Chong, Stanislaw H. Zak, An Introduction to Optimization, Third Edition, John Wiley and Sons, 2008 | |
| 3. Amir Beck, Introduction to Nonlinear Optimization: Theory, Algorithms and Applications with MATLAB, SIAM, 2014. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Ability to apply the acquired knowledge in mathematics, science and engineering | X | ||||
| 2 | Ability to identify, formulate and solve complex engineering problems | X | ||||
| 3 | Ability to accomplish the integration of systems | |||||
| 4 | Ability to design, develop, implement and improve complex systems, components, or processes | X | ||||
| 5 | Ability to select/develop and use suitable modern engineering techniques and tools | X | ||||
| 6 | Ability to design/conduct experiments and collect/analyze/interpret data | |||||
| 7 | Ability to function independently and in teams | |||||
| 8 | Ability to make use of oral and written communication skills effectively | |||||
| 9 | Ability to recognize the need for and engage in life-long learning | |||||
| 10 | Ability to understand and exercise professional and ethical responsibility | |||||
| 11 | Ability to understand the impact of engineering solutions | X | ||||
| 12 | Ability to have knowledge of contemporary issues | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 2 | 8 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 16 | 32 |
| Prepration of Final Exams/Final Jury | 1 | 20 | 20 |
| Total Workload | 150 | ||