Nonlinear Optimization (MDES656) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Nonlinear Optimization MDES656 Elective Courses 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English
Course Type Elective Courses Taken From Other Departments
Course Level Ph.D.
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
Major Area Courses X
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 Gains the ability to understand and apply knowledge in the fields of mathematics, science and basic sciences at the level of expertise.
2 Gains the ability to access wide and deep knowledge in the field of Engineering by doing scientific research with current techniques and methods, evaluate, interpret and implement the gained knowledge.
3 Being aware of the latest developments his/her field of study, defines problems, formulates and develops new and/or original ideas and methods in solutions.
4 Designs and applies theoretical, experimental, and model-based research, analyzes and interprets the results obtained at the level of expertise.
5 Gains the ability to use the applications, techniques, modern tools and equipment in his/her field of study at the level of expertise.
6 Designs, executes and finalizes an original work process independently.
7 Can work in interdisciplinary and interdisciplinary teams, lead teams, use the information of different disciplines together and develop solution approaches.
8 Pays regard to scientific, social and ethical values in all professional activities and acquires responsibility consciousness at the level of expertise.
9 Contributes to the literature by communicating the processes and results of his/her academic studies in written form or orally in national and international academic environments, communicates effectively with communities and scientific staff working in the field of specialization.
10 Gains the skill of lifelong learning at the level of expertise.
11 Communicates verbally and in written form using a foreign language at least at the European Language Portfolio B2 General Level.
12 Recognizes the social, environmental, health, safety, legal aspects of engineering applications, as well as project management and business life practices, being aware of the limitations they place on engineering applications.

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