この講義では,計算数理の基礎となる数学理論および計算手法,特に最適化の理論と手法を中心に解説し,最近の応用についてもふれる。
This course will cover some recent topics in the theory and applications of optimizations. This year,
topics will include semidefinite programming, gradient based methods, and constraint programming.
Part 1 Semidefinte Programming
1. Theory
2. Primal-Dual Interior-Point Methods
3. Some Applications
4. Linear Optimization Problems over Symmetric Cones
Part 2 Gradient Based Methods
1. Classical gradient, conjugate gradient, and Newton methods
2. Nestero
M. J. Todd, Semidefinite optimization, Acta Numerical 10 (2001) 515-560.
L. Vandenberghe and S. Boyd, Semidefinite Programming, SIAM Review 38 (1996) 49-95.
Yu. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course. Kluwer Academic
Basic linear algebra and analysis.
Reports and examinations.