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 Coordinator
Course Lecturer(s)
Course Assistants
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; understand the fundamentals of optimization understand the fundamental mathematical theory of linear and nonlinear programming understand the fundamental mathematical theory of constraint and unconstraint optimization choose and apply mathematical and computational tools to solve an optimization problem use MATLAB to understand the mathematical theory of optimization
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
#	Program Qualifications / Competencies	1	2	3	4	5
1	Gains sufficient knowledge in subjects specific to mathematics, natural sciences, and engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields to solve complex engineering problems.
2	Defines, formulates, and solves complex engineering problems; selects and applies appropriate analysis and modeling methods for this purpose.
3	Designs a complex system, process, device, or product under realistic constraints and conditions to meet specific requirements; applies modern design methods.
4	Selects and uses modern techniques and tools necessary for analyzing and solving complex problems encountered in engineering applications; gains the ability to use information technologies effectively.
5	Designs experiments, conducts experiments, collects data, and analyzes and interprets the results for studying complex engineering problems or research topics specific to engineering disciplines.
6	Works effectively in both disciplinary and multidisciplinary teams; gains the ability to work individually.
7	Develops effective oral and written communication skills; acquires proficiency in at least one foreign language; writes effective reports and understands written reports, prepares design and production reports, delivers effective presentations, and gives and receives clear and understandable instructions.
8	Develops awareness of the necessity of lifelong learning; gains access to information, follows developments in science and technology, and continuously renews oneself.
9	Acts in accordance with ethical principles, takes professional and ethical responsibility, and possesses knowledge of standards used in engineering applications.
10	Gains knowledge of business practices such as project management, risk management, and change management; develops awareness of entrepreneurship and innovation; possesses knowledge of sustainable development.
11	Gains knowledge of the impacts of engineering applications on health, environment, and safety in universal and societal dimensions, and the issues reflected in contemporary engineering fields; develops awareness of the legal consequences of engineering solutions.
12	Gains the ability to work in both thermal and mechanical systems fields, including the design and implementation of such systems.

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