- 担当教員
- 福田 光浩
- 使用教室
- 金7-8(W832)
- 単位数
- 講義：2 演習：0 実験：0
- 講義コード
- 75049
- シラバス更新日
- 2014年3月18日
- 講義資料更新日
- 2014年7月25日
- アクセス指標
-
- 学期
- 前期
講義概要
The main focus of this course is on algorithms to solve convex optimization problems which have recently gained some attention in continuous optimization. The course starts with basic theoretical results and then well-known algorithms will be analyzed and discussed.
講義の目的
Algorithms to solve large-scale convex optimization problems have been recently an important topic in continuous optimization. This lecture intends to provide basic mathematical tools to understand these algorithms focusing on computational aspects when solving large-scale problems.
講義計画
(tentative)
1. Convex sets and related results
2. Properties of Lipschitz continuous differentiable functions
3. Optimality conditions for differentiable functions
4. Complexity analysis of algorithms for minimizing unconstrained functions
5. Properties of convex differentiable functions
6. Worse cases for gradient based methods
7. Steepest descent methods for differentiable convex and differentiable strongly convex functions
8. Accelerated gradient methods
教科書・参考書等
D. P. Bertsekas, Nonlinear Programming, 2nd edition, (Athena Scientific, Belmont, Massachusetts, 2003).
D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 3rd edition, (Springer, New York, 2008).
O. L. Mangasarian, Nonlinear Programming, (SIAM, Philadelphia, PA, 1994).
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, (Kluwer Academic Publishers, Boston, 2004).
J. Nodedal and S. J. Wright, Numerical Optimization, 2nd edition, (Springer, New York, 2006).
関連科目・履修の条件等
It is necessary to have basic knowledge of linear algebra, calculus, topology and computational complexity.
成績評価
Final exam and/or reports.
