COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Nonlinear Programming
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
IES 534
Fall/Spring
3
0
3
7.5
Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
Second Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives The aim of this course is to develop knowledge of different theoretical aspects of nonlinear programming and convex optimization and to give graduate and PhD students the theoretical background on convex analysis and on the theory of optimality conditions, and to provide them with a foundation sufficient to use basic optimization in their own research work and/or to pursue more specialized studies involving optimization theory.
Learning Outcomes The students who succeeded in this course;
  • Will be able to interpret convex sets and convex functions
  • Will be able to analyze extreme points and extreme directions of convex sets
  • Will be able to analyze some topological properties of convex sets and convex functions
  • Will be able to use the concept of convexity in the analysis of nonlinear programming problems
  • Will be able to interpret optimality conditions for nonlinear programming problems
Course Description The course emphasizes the unifying themes such that convex sets and convex functions, their topological properties, separation theorems and optimality conditions for convex optimization problems.
Related Sustainable Development Goals

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 GirişIntroduction.
2 Dışbükey kümeler. Dışbükey örtü. Caratheodory Teoremi.Convex sets. Convex hull. Caratheodory Theorem.
3 Bir kümenin kapanış ve iç noktaları. Weierstrass’ Teoremi.Closure and interior of a set. Weierstrass’ Theorem
4 İki kümenin ayrılması. Destek yüzeyi kavramı.Separation of two sets. The notion of supporting surface.
5 Koni. Cone.
6 Polihedral kümeler. Uç nokta ve uç yönler.Polihedral sets. Extreme points and extreme directions.
7 Dışbükey fonksiyonlar. Tanımlar ve temel özellikler.Convex functions. Definitions and basic properties.
8 Yönlü türev.Directional derivative.
9 Subgradient.Subgradient.
10 Diferansiyellenebilen dışbükey fonksiyonlar.Differentiable convex functions.
11 Minima and maxima of convex functions.Dışbükey fonksiyonların minimum ve maksimumları
12 Kısıtsız optimizasyon problemleri için eniyilik koşulları.Optimality conditions for unconstrained optimization problems.
13 Kısıtlı optimizasyon problemleri için Fritz John eniyilik koşulları.The Fritz John optimality conditions for constrained optimization problems.
14 Kısıtlı optimizasyon problemleri için KarushKuhnTucker eniyilik koşulları.The KarushKuhnTucker optimality conditions for constrained optimization problems.
15 Uygulamalar.Applications.
16 Review of the Semester  
Course Notes/Textbooks Nonlinear Programming. Theory and Algorithms., Mokhtar S. Bazaraa, Hanif D. Sherali, C.M. Shetty, John Wiley & Sons, ISBN 0471557935.
Suggested Readings/Materials Bertsekas, D. Nonlinear Programming, Second Edition, Athena Scientific Publishing, 1999.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
4
10
Presentation / Jury
1
15
Project
Seminar / Workshop
Oral Exam
Midterm
2
45
Final Exam
1
30
Total

Weighting of Semester Activities on the Final Grade
70
Weighting of End-of-Semester Activities on the Final Grade
30
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
8
120
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
4
6
Presentation / Jury
1
6
Project
Seminar / Workshop
Oral Exam
Midterms
2
10
Final Exams
1
15
    Total
233

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

3

To have the ability of defining and verifying problems in Mathematics and Statistics,

4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest