2020 Numerical Optimization

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Academic unit or major
Graduate major in Industrial Engineering and Economics
Mizuno Shinji  Nakata Kazuhide 
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Tue5-6(Zoom)  Fri5-6(Zoom)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

This course treats interior point methods for solving linear programming. Especially, students acquire with mathematical theory, optimal condition, polynomial convergence, and computational efficiency of interior point methods.
In addition, this course teats techniques to mining useful knowledge from Japanese documents. Especially, students study various methods of separating words and word embedding.

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 separation words and word embedding for Japanese documents and can apply them to real problems.


Interior-point method, Linear programming, Text mining

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 Linear programming We instruct in each class
Class 2 Primal interior-point method (affine scaling algorithm)
Class 3 Primal interior-point method (Karmarkar's algorithm)
Class 4 Analytic center and center path
Class 5 Primal-dual interior-point method (affine scaling algorithm)
Class 6 Primal-dual interior-point method (path following mathed)
Class 7 Infeasible interior-point method
Class 8 Japanese documents
Class 9 Separating words
Class 10 Implementation preparation
Class 11 Implementation of Separating words
Class 12 Word embedding
Class 13 Word2Vec
Class 14 Implementation of Word2Vec

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


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

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites

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