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 | Possesses sufficient knowledge in mathematics, natural sciences, and discipline-specific topics in Electrical and Electronics Engineering; uses this theoretical and practical knowledge to solve complex engineering problems. | X | ||||
| 2 | Identifies, defines, formulates, and solves complex engineering problems; selects and applies appropriate analytical and modeling methods for this purpose. | X | ||||
| 3 | Designs complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements; applies modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, depending on the nature of the design.) | X | ||||
| 4 | Selects and uses modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications; effectively uses information technologies. | |||||
| 5 | Designs experiments, conducts tests, collects data, analyzes, and interprets results to investigate complex engineering problems or discipline-specific research topics. | |||||
| 6 | Works effectively in disciplinary and interdisciplinary teams; develops the ability to work independently. | |||||
| 7 | Communicates effectively in both written and verbal forms; possesses proficiency in at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, delivers effective presentations, and gives and receives clear instructions. | |||||
| 8 | Recognizes the need for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself. | |||||
| 9 | Acts in accordance with ethical principles, assumes professional and ethical responsibility, and possesses knowledge about the standards used in engineering practices. | |||||
| 10 | Possesses knowledge about professional practices such as project management, risk management, and change management; gains awareness of entrepreneurship and innovation; understands the principles of sustainable development. | |||||
| 11 | Understands the universal and societal impacts of engineering practices on health, environment, and safety; recognizes the contemporary issues reflected in the field of engineering and understands the legal implications of engineering solutions. | |||||
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 | ||