| Course Name | Nonlinear Programming |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| IE 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;
|
| 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 | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Intrıduction | |
| 2 | Convex sets. Convex hull. Caratheodory Theorem. | |
| 3 | Closure and interior of a set. Weierstrass’ Theorem | |
| 4 | Separation of two sets. The notion of supporting surface. | |
| 5 | Cone. | |
| 6 | Polihedral sets. Extreme points and extreme directions. | |
| 7 | Convex functions. Definitions and basic properties. | |
| 8 | Directional derivative. | |
| 9 | Subgradient. | |
| 10 | Differentiable convex functions. | |
| 11 | Minima and maxima of convex functions. | |
| 12 | Optimality conditions for unconstrained optimization problems. | |
| 13 | The Fritz John optimality conditions for constrained optimization problems. | |
| 14 | The KarushKuhnTucker optimality conditions for constrained optimization problems. | |
| 15 | 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. |
| 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 |
| 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 | 14 | 8 | 112 |
| 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 | 225 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information. | X | ||||
| 2 | Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations. | X | ||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines. | X | ||||
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. | X | ||||
| 5 | Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions. | X | ||||
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. | X | ||||
| 7 | Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process. | X | ||||
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility. | X | ||||
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. | X | ||||
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. | X | ||||
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications. | X | ||||
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
