EEE5010 OptimizationBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, NON-THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, NON-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
EEE5010 Optimization Spring 3 0 3 9
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: English
Type of course: Must Course
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. SÜREYYA AKYÜZ
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
Recommended Optional Program Components: None
Course Objectives: To equip students with the mathematical theory of optimization and solution methods.

Learning Outcomes

The students who have succeeded in this course;
Students will
- be able to formulate optimization problems
- understand basic differences between various constraints
- apply numerical techniques to solve optimization problems

Course Content

Optimization as a decision making problem. Optimization over an open set. Optimization under equality constraints; Lagrange multipliers. Optimization under inequality constraints. Linear programming. Numerical methods.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) The Optimization Problem. Examples.
2) Mathematical preliminaries
3) Mathematical preliminaries
4) The Weierstrass Theorem. Application to example problems.
5) Optimization over an open set. Necessary and sufficient conditions.
6) Numerical techniques: Gradient algorithm, Newton's method.
8) Optimization with equality constraints. Lagrange multipliers.
9) Optimization with inequality constraints. Kuhn-Tucker conditions.
10) Linear programming: Standard maximization and minimization problems.
11) Linear programming: Primal and dual problems. Duality theorem. Optimality conditions.
12) The Simplex algorithm.
13) Discrete dynamic programming.
14) Large optimization problems. Decomposition methods.

Sources

Course Notes / Textbooks: 1. P. Varaia, Lecture Notes on Optimization, web
References: 1. C.T. Kelley, Iterative Methods for Optimization, SIAM

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 5 % 25
Midterms 1 % 25
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Workload
Course Hours 14 42
Study Hours Out of Class 16 136
Homework Assignments 5 10
Midterms 1 2
Final 1 2
Total Workload 192

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.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
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) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
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 apply mathematical principles to real world problems.
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.