MAT5016 OptimizationBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5016 Optimization Spring 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. SÜREYYA AKYÜZ
Recommended Optional Program Components: None
Course Objectives: The objective of this course is to introduce the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed.

Learning Outcomes

The students who have succeeded in this course;
At the end of this course students should be able to tackle optimization problems of in science, engineering and finance using state of art numerical methods.

Course Content

In this course the solution of unconstrained and constrained optimization problem will be discussed.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Unconstrained Optimization
2) Newton Methods
3) Linear Search Methods
4) Trust Region Method
5) Quasi Newton Methods
6) Non linear least squares method
7) Theory of Constrained Optimization
8) Theory of Linear Programming
9) Simplex Method
10) Interior Point Methods
11) Interior Point Methods
12) Penalty and Barrier Methods
13) Sequential Quadratic Programming
14) Conclusion and Outlook of Constrained and Unconstrained Optimization

Sources

Course Notes / Textbooks: Lecture Notes are prepared by B. Karasözen and G.-W. Weber and available from IAM Lecture Notes Series, METU, Ankara.
G. Nash and Ariela Sofer, Linear and nonlinear programming, New York : McGraw-Hill, 1996, T57.74 N37
J. Nocedal, S.J. Wright, Numerical Optimization, Springer, 1999, QA 402.5 N62
References: S. Ulbrich, M. Ulbrich, “Nonlinear Optimization”, Lecture Notes, Department of Mathematics, University of Technology Darmstadt,

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 14 % 0
Homework Assignments 3 % 20
Project 1 % 20
Midterms 1 % 30
Final 1 % 30
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other. 3
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. 3
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. 4
4) Ability to make individual and team work on issues related to working and social life. 3
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. 2
6) Ability to use mathematical knowledge in technology. 4
7) To apply mathematical principles to real world problems. 2
8) Ability to use the approaches and knowledge of other disciplines in Mathematics. 3
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. 3
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,