Linear Optimization (MDES655) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Linear Optimization	MDES655	Area Elective	3	0	0	3	5

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Elective Courses
Course Level	Ph.D.
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	This course aims to give to Ph.D. students from different engineering backgrounds the skills of real life problem formulation with linear optimization along with the use of basic computer packages to solve the problems.
Course Learning Outcomes	The students who succeeded in this course; 1. Students will have a vision of linear optimization and duality. 2. Students will get a perspective of linear optimization algorithms and be able to code and implement algorithms. 3. Students will develop a vision of the application areas of linear optimization. 4. Students will have a knowledge of decomposition techniques especially for large scaled linear optimization problems. 5. Students will be familiarized with algorithmic complexity and convergence issues.
Course Content	Sets of linear equations, linear feasibility and optimization, local and global optima, the Simplex method and its variants, theory of duality and the dual-Simplex method, network-Simplex algorithms, computational complexity issues and interior-point algorithms.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	An introduction to linear feasibility and linear optimization problems.	Related pages of the textbook and other courses
2	Geometry of linear optimization, polyhedral sets, extreme points and basic feasible solutions.	Related pages of the textbook and other courses
3	The Simplex Algorithm.	Related pages of the textbook and other courses
4	Duality theory and complementary slackness.	Related pages of the textbook and other courses
5	Sensitivity analysis and parametric linear programming.	Related pages of the textbook and other courses
6	The Dual Simplex Algorithm.	Related pages of the textbook and other courses
7	Extensions of the Simplex Method. Simplex with upper and lower bounds.	Related pages of the textbook and other courses
8	Midterm	-
9	Algorithms with sparse matrices and decomposition techniques.	Related pages of the textbook and other courses
10	The network-flow problems and the Network Simplex Method.	Related pages of the textbook and other courses
11	Application issues of linear optimization.	Related pages of the textbook and other courses
12	Algorithmic complexity of the Simplex Method.	Related pages of the textbook and other courses
13	The ellipsoid method and an overview of interior-point algorithms.	Related pages of the textbook and other courses
14	Algorithm coding and presentations.	Related pages of the textbook and other courses
15	Overall review	-
16	Final exam	-

Sources

Course Book	1. [1] S.G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw Hill 1996.
Other Sources	2. [2] V. Chvatal, Linear Programming, Freeman 1983.
	3. [3] G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, Wiley 1988.
	4. [4] H.P. Williams, Model Building in Mathematical Programming, 2nd edition, Wiley, 1985.
	5. [5] F.S. Hillier and G.J. Lieberman, Introduction to Mathematical Programming, 2nd edition, McGraw-Hill, 1995.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	1	15
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	3	25
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	1	30
Final Exam/Final Jury	1	30
Toplam	6	100

Percentage of Semester Work	70
Percentage of Final Work	30
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	Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir				X
2	Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur.					X
3	Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir			X
4	Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir				X
5	Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir.				X
6	Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir			X
7	Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir.				X
8	Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur.				X
9	Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir.				X
10	Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir.				X

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	1	20	20
Field Work
Study Hours Out of Class	16	2	32
Presentation/Seminar Prepration
Project
Report
Homework Assignments	3	6	18
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	1	8	8
Prepration of Final Exams/Final Jury	1	10	10
Total Workload			136