MATH 316 | Course Introduction and Application Information - Department of Mathematics

Course Name

Optimization II

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 316	Spring	3	0	3	6

Prerequisites

MATH 305 To succeed (To get a grade of at least DD)

Course Language

English

Course Type

Required

Course Level

First Cycle

Mode of Delivery

-

Teaching Methods and Techniques of the Course

Group Work
Problem Solving
Lecture / Presentation

National Occupation Classification

-

Course Coordinator

-

Course Lecturer(s)

Prof. Dr. Gözde Yazgı TÜTÜNCÜ

Assistant(s)

Course Objectives

This course provides an introduction to some concepts of the field of optimization and presents various optimization methods in order to solve some nonlinear optimization problems. Topics include: modeling of non-linear and integer programming and several solving methods. The course provides many examples of most common non-linear optimization methods, integer programming methods and assumptions lead to useful comprehension of applied mathematics problems

Learning Outcomes

The students who succeeded in this course;

will be able to model real life problems using nonlinear programming(NLP).
will be able to solve problems using methods of NLP such as Lagrange multipliers method and The Branch-and-Bound Method.
will be able to classify NLPs with one variable and several variables.
will be able to solve pure integer and mixed integer programming.
will be able to compare the characterizations of optimization problems with equality and inequality constraints.

Course Description

This course aims to cover basic theory and applications of nonlinear optimization.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Modeling and formulation of non-linear optimization problems	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.1
2	Review of differential calculus for optimization	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.2, 3.4
3	Quadratic forms, Gradient vector, Hessian matrix, convex and concave functions	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.4, 4.3, 4.7
4	Solving NLPs with one variable	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.4
5	Unconstrained maximization and minimization with several variables	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 4.5
6	Optimization problems with equality constraints. Lagrange multipliers method	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.2
7	Optimization problems with equality constraints. Lagrange multipliers method	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.2
8	Optimization problems with inequality constraints. KKT optimality condition	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.3
9	Other nonlinear optimization problems, their characterizations and solution methods	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 3.5, 3.6, 3.7
10	Formulating integer programming problems	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 2.5
11	The Branch-and-Bound method for solving pure integer programming problems	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 2.5
12	The Branch-and-Bound method for solving pure integer programming problems	“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. Chapter 2.5
13	The Cutting Plane algorithm	“Operations Research: Applications and Algorithms” by Wayne L. Winston, Cengage Learning, 4th Edition, 2003. Chapter 9.8
14	Applying the Cutting Plane algorithm to optimization problems	“Operations Research: Applications and Algorithms” by Wayne L. Winston, Cengage Learning, 4th Edition, 2003. Chapter 9.8
15	Semester Review
16	Final Exam

Course Notes/Textbooks

“Introduction to Optimization” by Pablo Pedregal, Springer-Verlag New York, 1st Edition, 2004. ISBN-13: 978-0387403984

Suggested Readings/Materials

“Operations Research: Applications and Algorithms” by Wayne L. Winston, Cengage Learning, 4th Edition, 2003. ISBN-13: 978-0534380588

“A First Course in Optimization Theory” by R.K. Sundaram, Cambridge Press,1st Edition, 1996. ISBN-13: 978-0521497701

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury	1	10
Project	1	20
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	3	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	15	15
Project	1	20	20
Seminar / Workshop			0
Oral Exam			0
Midterms	1	25	25
Final Exam	1	30	30
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	-	-
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	-	X	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	-	X
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	X	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-