# Nonlinear Optimization (MDES656) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Nonlinear Optimization MDES656 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English Focus Course Ph.D. Face To Face Lecture. This course aims to give to Ph.D. students from different engineering backgrounds the theory of nonlinear optimization along with possible application areas. The students who succeeded in this course; 1. Students will have a vision of the theory of nonlinear optimization as well as understanding of algorithms. 2. Students will be able to read and make mathematical proofs. 3. Students will have an understanding of algorithmic complexity and convergence. 4. Students will develop a vision of the application areas of nonlinear optimization. 5. Students will acquire the ability to summarize a mathematical paper in front of an audience. Linear algebra and polyhedral sets, duality and the theorems of the alternative, convex sets and convex functions, line-search methods, unconstrained optimization, optimality conditions; steepest descent, Newton, quasi-Newton and conjugate-gradient algorithms; constrained optimization and optimality conditions; the reduced gradient method; penalty

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 A review of linear algebra, duality and theorems of the alternative. Related pages of the textbook and other courses
2 Convexity, convex sets, cones, extreme points and extreme directions. Related pages of the textbook and other courses
3 Separating hyperplanes, supporting hyperplanes, convex functions. Related pages of the textbook and other courses
4 Linear optimization, quadratic optimization and convex optimization. Related pages of the textbook and other courses
5 Constrained/unconstrained optimization and line search techniques. Related pages of the textbook and other courses
6 Necessary/sufficient conditions of optimality. Related pages of the textbook and other courses
7 Primal algorithms, feasible moving directions and step size selection. Related pages of the textbook and other courses
8 Steepest descent and Newton algorithms. Variants of Newton algorithms. Related pages of the textbook and other courses
9 Midterm Related pages of the textbook and other courses
10 Conjugate gradients algorithm Related pages of the textbook and other courses
11 Methods for constrained optimization problems. Related pages of the textbook and other courses
12 Nonlinear approaches to linear optimization problems. Related pages of the textbook and other courses
13 Issues of convergence Related pages of the textbook and other courses
14 Paper presentations. Related pages of the textbook and other courses
15 Overall review -
16 Final exam -

### Sources

Course Book 1. S.G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw Hill, 1996. 2. M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, Nonlinear Programming (2nd ed.), Wiley, 1993 3. D.P. Bertsekas, Nonlinear Programming, Athena Scientific, 1995 4. J. Shapiro, Mathematical Programming, Wiley, 1979. 5. R.L. Rardin, Optimization in Operations Research, Prentice-Hall, 1998. 6. F.S. Hillier and G.J. Lieberman, Introduction to Mathematical Programming, 2nd edition, McGraw-Hill, 1995.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 25
Presentation 1 15
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 30
Toplam 6 100
 Percentage of Semester Work 70 30 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration 1 20 20
Project
Report
Homework Assignments 3 6 18
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 8 8
Prepration of Final Exams/Final Jury 1 10 10