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 computing fields; ability to apply theoretical and practical knowledge of these fields in solving engineering problems related to information systems. | |||||
| 2 | Ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; ability to apply modern design methods for this purpose. | |||||
| 4 | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in information systems engineering applications; ability to use information technologies effectively. | |||||
| 5 | Ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the information systems discipline. | |||||
| 6 | Ability to work effectively in inter/inner disciplinary teams; ability to work individually. | |||||
| 7 | a. Effective oral and written communication skills in Turkish; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. b. Knowledge of at least one foreign language; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |||||
| 8 | Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development. | |||||
| 9 | a. Ability to behave according to ethical principles, awareness of professional and ethical responsibility. b. Knowledge of the standards utilized in information systems engineering applications. | |||||
| 10 | a. Knowledge on business practices such as project management, risk management and change management. b. Awareness about entrepreneurship, and innovation. c. Knowledge on sustainable development. | |||||
| 11 | a. Knowledge of the effects of information systems engineering applications on the universal and social dimensions of health, environment, and safety. b. Awareness of the legal consequences 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 | ||