- Lecturer
- Fukuda Mituhiro
- Place
- Fri7-8(W832)
- Credits
- Lecture2 Exercise0 Experiment0
- Code
- 75049
- Syllabus updated
- 2014/3/18
- Lecture notes updated
- 2014/7/25
- Access Index
-
- Semester
- Spring Semester
Outline of lecture
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.
Purpose of lecture
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.
Plan of lecture
(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
Textbook and reference
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).
Related and/or prerequisite courses
It is necessary to have basic knowledge of linear algebra, calculus, topology and computational complexity.
Evaluation
Final exam and/or reports.
