ECTS - Linear Optimization
Linear Optimization (MDES655) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Linear Optimization | MDES655 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| Course Objectives | This course aims to give to Ph.D. students from different engineering backgrounds the skills of real life problem formulation with linear optimization along with the use of basic computer packages to solve the problems. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Sets of linear equations, linear feasibility and optimization, local and global optima, the Simplex method and its variants, theory of duality and the dual-Simplex method, network-Simplex algorithms, computational complexity issues and interior-point algorithms. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | An introduction to linear feasibility and linear optimization problems. | Related pages of the textbook and other courses |
| 2 | Geometry of linear optimization, polyhedral sets, extreme points and basic feasible solutions. | Related pages of the textbook and other courses |
| 3 | The Simplex Algorithm. | Related pages of the textbook and other courses |
| 4 | Duality theory and complementary slackness. | Related pages of the textbook and other courses |
| 5 | Sensitivity analysis and parametric linear programming. | Related pages of the textbook and other courses |
| 6 | The Dual Simplex Algorithm. | Related pages of the textbook and other courses |
| 7 | Extensions of the Simplex Method. Simplex with upper and lower bounds. | Related pages of the textbook and other courses |
| 8 | Midterm | - |
| 9 | Algorithms with sparse matrices and decomposition techniques. | Related pages of the textbook and other courses |
| 10 | The network-flow problems and the Network Simplex Method. | Related pages of the textbook and other courses |
| 11 | Application issues of linear optimization. | Related pages of the textbook and other courses |
| 12 | Algorithmic complexity of the Simplex Method. | Related pages of the textbook and other courses |
| 13 | The ellipsoid method and an overview of interior-point algorithms. | Related pages of the textbook and other courses |
| 14 | Algorithm coding and presentations. | Related pages of the textbook and other courses |
| 15 | Overall review | - |
| 16 | Final exam | - |
Sources
| Course Book | 1. [1] S.G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw Hill 1996. |
|---|---|
| Other Sources | 2. [2] V. Chvatal, Linear Programming, Freeman 1983. |
| 3. [3] G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, Wiley 1988. | |
| 4. [4] H.P. Williams, Model Building in Mathematical Programming, 2nd edition, Wiley, 1985. | |
| 5. [5] 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 | 1 | 15 |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 25 |
| Presentation | - | - |
| 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 | An ability to solve mathematically defined advanced engineering problems analytically. | |||||
| 2 | An ability to solve mathematically defined advanced engineering problems numerically. | X | ||||
| 3 | An ability to use the technology and the literature effectively in the civil engineering research domain. | |||||
| 4 | An ability to conduct qualitative research in civil engineering and publish articles in conferences and journals in the area. | |||||
| 5 | Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process. | X | ||||
| 6 | To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | 1 | 20 | 20 |
| Field Work | |||
| Study Hours Out of Class | 16 | 2 | 32 |
| Presentation/Seminar Prepration | |||
| 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 | ||