ECTS - Nonlinear Optimization
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) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| Course Objectives | This course aims to give to Ph.D. students from different engineering backgrounds the theory of nonlinear optimization along with possible application areas. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | 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. |
|---|---|
| Other Sources | 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
| Requirements | Number | Percentage of Grade |
|---|---|---|
| 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 |
|---|---|
| Percentage of Final Work | 30 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
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 | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
ECTS/Workload Table
| 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 |
| Total Workload | 136 | ||