ECTS - Nonlinear Optimization
Nonlinear Optimization (MDES656) Course Detail
Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
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Nonlinear Optimization | MDES656 | 3 | 0 | 0 | 3 | 5 |
Pre-requisite Course(s) |
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Consent of the instructor |
Course Language | English |
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Course Type | N/A |
Course Level | Natural & Applied Sciences Master's Degree |
Mode of Delivery | Face To Face |
Learning and Teaching Strategies | Lecture. |
Course Lecturer(s) |
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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;
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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 |
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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. |
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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 |
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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 |
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Percentage of Final Work | 30 |
Total | 100 |
Course Category
Core Courses | X |
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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 | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | Ability to expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement. | |||||
2 | Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering. | |||||
3 | To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines. | |||||
4 | Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed. | |||||
5 | Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions. | |||||
6 | Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs. | |||||
7 | Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process. | |||||
8 | Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility. | |||||
9 | To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level. | |||||
10 | Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments. | |||||
11 | To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications. | |||||
12 | Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities. |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |