COURSE INTRODUCTION AND APPLICATION INFORMATION

Course Name
Optimization
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 305
Fall
3
0
3
7
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery face to face
Teaching Methods and Techniques of the Course Problem Solving
Practical demonstration
Lecturing / Presentation
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives The objective of this course is to provide a deep understanding of mathematical aspects of linear programming (LP).
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 and the simplex method.
  • will be able to analyze shadow prices using Duality theorem.
  • will be able to inspect LPs with sensitivity analysis.
  • will be able to build unconstrained and nonlinear optimization models.
  • will be able to solve problems modeled with unconstrained and nonlinear optimization models.
Course Description This course aims to cover basic theory and applications of linear optimization.
Related Sustainable Development Goals

 



Course Category

 Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 The concept of Optimization. Modeling and formulation of Optimization problems Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 1
2 Linear programming (LP) Solutions of an LP problem: Geometric method Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 2, Chapter 3
3 Solutions of an LP problem: Analytic Method Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 3
4 Solutions of an LP problem: Simplex Method Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 4
5 Simplex Table, Duality Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 4
6 Quadratic forms, Gradient Vector and Hessian Matrix Convex and concave functions Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 4
7 Unconstraint Optimization Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 11
8 Midterm
9 Nonlinear optimization problems Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 11
10 Nonlinear optimization problems Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 11
11 Project Presentations
12 Constraint Optimization Discriminant method Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 3
13 Lagrange multipliers Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 11
14 KuhnTucker conditions Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 11
15 Semester review
16 Final exam
Course Notes/Textbooks

Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588
Suggested Readings/Materials

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

''A first Course in Optimization Theory'' by R.K.Sundaram, Cambridge Press, First Edition, 1996. ISBN-13: 978-0521497701 

“An Introduction to Optimization” by Edwin K.P. Chong and Stanislaw H. Zak, Wiley, 2nd Edition, 2001. ISBN-13: 978-0471391265

 

 

EVALUATION SYSTEM

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

Weighting of Semester Activities on the Final Grade
4
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
14
4
56
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
1
18
Project
1
18
Seminar / Workshop
Oral Exam
Midterms
1
30
Final Exams
1
40
    Total
210

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

 X
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.
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.

 X
5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

 X
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.
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.

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