Nonlinear Optimization (MDES656) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Nonlinear Optimization MDES656 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English
Course Type N/A
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
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;
  • 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.
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 -


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 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
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration 1 20 20
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