 MECHATRONICS ENGINEERING (ENGLISH, NONTHESIS) 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 Fall 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: Departmental Elective 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