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 | Bachelor’s Degree (First Cycle) |
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
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 | ||