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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | |||||
| 2 | Ability to formulate, and solve complex mechatronics engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | |||||
| 3 | Ability to design a complex mechatronics engineering system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | |||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in mechatronics engineering and robot technology practices; ability to employ information technologies effectively. | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex mechatronics engineering and robot technology problems or research questions. | |||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | |||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | |||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself | |||||
| 9 | a-) Knowledge on behavior according to ethical principles, professional and ethical responsibility b-) Knowledge on standards used in engineering practices. | |||||
| 10 | a-) Knowledge about business life practices such as project management, risk management, and change management b-) Awareness in entrepreneurship, innovation; knowledge about sustainable development. | |||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | |||||
| 12 | Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions in the field of mechatronics engineering. | |||||
| 13 | Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planning, improving or changing the norms with a criticism. | |||||
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 | ||