- School of Science
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- Group 2
- Group 3
- Group 4
- Group 5
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- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
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- Common Cource of Engineering

- School of Bioscience and Biotechnology
- Common Course of Undergraduate School

- Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
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- Graduate School of Bioscience and Biotechnology
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- Built Environment
- Energy Sciences
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- Materials Science and Engineering
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- Environmental Chemistry and Engineering
- Environmental Science and Technology
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- Information Processing
- Electronics and Applied Physics

- Graduate School of Information Science and Engineering
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- Common Course of Graduate School
- Program for Leading Graduate Schools

- Lecturer
- Fukuda Mituhiro

- Place
- Fri7-8(W832)

- Credits
- Lecture2 Exercise0 Experiment0

- Code
- 75049

- Syllabus updated
- 2015/3/16

- Lecture notes updated
- 2015/7/10

- Access Index

- Semester
- Spring Semester

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.

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.

(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

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).

It is necessary to have basic knowledge of linear algebra, calculus, topology and computational complexity.

Final exam and/or reports.