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.
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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Attendance is taken in every class.
Students are required to read the text before coming to class.
|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|
Course materials can be found on OCW-i
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%).