### 2017　Numerical Optimization

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Graduate major in Industrial Engineering and Economics
Instructor(s)
Mizuno Shinji  Nakata Kazuhide
Course component(s)
Lecture
Mode of instruction

Day/Period(Room No.)
Tue5-6(西9号館, 414号室)  Fri5-6(西9号館, 414号室)
Group
-
Course number
IEE.A430
Credits
2
2017
Offered quarter
3Q
Syllabus updated
2017/3/17
Lecture notes updated
2017/9/25
Language used
Japanese
Access Index

### Course description and aims

This course treats interior point methods for solving linear programming and cone programming problems. Especially, students acquire with mathematical theory, optimal condition, polynomial convergence, and computational efficiency of interior point methods.

### Student learning outcomes

By the end of this course, students will be able to:
1. Understand the theoretical properties of interior-point methods for linear programming problems and can apply them to real problems.
2. Understand the theoretical properties of interior-point methods for conic programming problems and can apply them to real problems.

### Keywords

Interior-point method, Linear programming, Symmetric cone programming

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Attendance is taken in every class.
Students are required to read the text before coming to class.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Overview of optimization We instruct in each class
Class 2 Linear programming
Class 3 Primal interior-point method (affine scaling algorithm)
Class 4 Primal interior-point method (Karmarkar's algorithm)
Class 5 Analytic center and center path
Class 6 Primal-dual interior-point method (affine scaling algorithm)
Class 7 Primal-dual interior-point method (path following mathed)
Class 8 Infeasible interior-point method
Class 9 Euclidean Jordan algebra
Class 10 Properties of Euclidean Jordan algebra
Class 11 Symmetric cone
Class 12 Symmetric cone programming
Class 13 Duality theorem and optimal condition
Class 14 Primal-dual interior-point method
Class 15 Efficient computation

None required

### Reference books, course materials, etc.

Course materials can be found on OCW-i

### Assessment criteria and methods

Students will be assessed on their understanding of interior point method, and their ability to apply them to solve problems.
Students' course scores are based on reports (50%) and mini exams (50%).

### Related courses

• IEE.A206 ： Operations Research
• IEE.A330 ： Advanced Operations Research
• IEE.A331 ： OR and Modeling

No prerequisites