2017 Numerical Optimization

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Graduate major in Industrial Engineering and Economics
Mizuno Shinji  Nakata Kazuhide 
Course component(s)
Day/Period(Room No.)
Tue5-6(西9号館, 414号室)  Fri5-6(西9号館, 414号室)  
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 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.


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

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

No prerequisites

Page Top