GRADUATE SCHOOL

M.SC. in Computer Engineering (With Thesis)

MATH 553 | Course Introduction and Application Information

Course Name
Optimization
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 553
Fall/Spring
3
0
3
7.5

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
Second Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives
Upon the completion of this course the student expected to gain an aiding tool for solving realworld problems which require LP approach, be able to have a detailed information about fundamental methods of LP such as Graphical method and the simplex method. Students will have detailed information about Duality and Sensitivity of L.P's. They will have information on unconstraint and nonlinear optimization models and methods to solve this problem.
Learning Outcomes The students who succeeded in this course;
  • will be able to model real life problems using Linear programming(LP).
  • will be able to solve problems using methods of LP such as Graphical method, the simplex method and BigM method..
  • will be able to analyze dual problem and marginal costs using Duality theorem.
  • will be able to inspect optimization problems with Sensitivity analysis.
  • will be able to develop unconstraint and nonlinear optimization models.
  • will be able to solve unconstraint and nonlinear optimization problems.
Course Description Linear Programming: Modeling, Solution Methods, Duality in linear programming; Nonlinear programming: First and second order optimality conditions for unconstrained problems, Lagrange multipliers, convexity in mathematical programming, The KuhnTucker theorem; Discrete optimization.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Basic Linear Algebra Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
2 Introduction to Linear Programming Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
3 The Simplex Algorithm Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
4 Sensitivity Analysis Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
5 Duality Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
6 Integer Programming Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
7 Advanced Topics in LP Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
8 Nonlinear Programming Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
9 Nonlinear Programming Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
10 Probablistic Inventory Models Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
11 Game Theory Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
12 Exam Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
13 Project Presentations Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
14 Project Presentations Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
15 Semester Review Operations Research Applications and Algorithms, W.L.Winston, 4th Edition , 2004. Introduction to Operations Research, 7th Edition, Hillier, Liberman, McGrawHill, 2001
16 Final Exam

 

Course Notes/Textbooks

"Operations Research Applications and Algorithms" by W.L.Winston, Duxbury Press 4th Edition , 1997, ISBN-13: 978-0534520205

Suggested Readings/Materials

"Introduction to Operations Research", 7th Edition, Hillier, Liberman, McGrawHill, 2001. ISBN-13: 978-0072461213

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
2
20
Project
1
20
Seminar / Workshop
Oral Exams
Midterm
2
25
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
5
65
Weighting of End-of-Semester Activities on the Final Grade
1
35
Total

ECTS / WORKLOAD TABLE

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
10
6
60
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
2
4
8
Project
1
9
9
Seminar / Workshop
0
Oral Exam
0
Midterms
2
25
50
Final Exam
1
50
50
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 Accesses information in breadth and depth by conducting scientific research in Computer Engineering; evaluates, interprets and applies information.
2 Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.
3 Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines.
4 Is informed about new and upcoming applications in the field and learns them whenever necessary.
5 Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.
6 Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs
7 Designs and implements studies based on theory, experiments and modelling; analyses and resolves the complex problems that arise in this process.
8 Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility.
9 Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.
10 Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.
11 Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.
12 Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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