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Optimization Lab
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A mathematics lab that seeks optimal solutions to problems in society, science, and engineering.
AboutAbout the lab
Mathematical theory and methods for finding optimal solutions.
In the field of optimization, the lab treats problems from social phenomena and from science and engineering as constrained extremum problems, and studies the mathematical theory and methods for finding their optimal solutions.
The faculty members' research includes optimization problems involving continuous variables, decision-making problems using dynamic programming, and the use of computer algebra and artificial intelligence.
Many of the faculty members belong to the Institute of Mathematics for Industry while also holding concurrent positions in the Department of Mathematics of the Faculty of Science and the Graduate School of Mathematics.
Key terms
- Optimization problem
- A problem of finding the solution, and its value, that maximizes or minimizes a function under given conditions or constraints
- Dynamic programming
- A method for efficiently solving problems that require repeated decision-making or that involve uncertainty
- Semidefinite programming problem
- A type of optimization problem. It is used to solve nonconvex, nonlinear optimization problems that are hard to solve directly
ResearchResearch themes
Optimization is a field that treats problems from social phenomena and from science and engineering as constrained extremum problems, and studies the mathematical theory and methods for finding their optimal solutions. The faculty members' research includes optimization problems involving continuous variables, dynamic programming, and computer algebra.
*Illustrative imageSolving Problems with Mathematical Techniques and Artificial Intelligence
The lab has tackled problems facing industry and society by using mathematical techniques and artificial intelligence such as machine learning. Centered on algorithms and applications of computer algebra, it also works on the automatic solving of mathematical problems.
*Illustrative imageOptimization Problems Involving Continuous Variables
The lab's research themes include semidefinite programming problems, within optimization problems that involve continuous variables. It is interested in investigating the structure and properties of the phenomena and problems under study through the properties of the optimization problems.
*Illustrative imageDynamic Programming and Social Mathematics
The lab studies the theory and applications of dynamic programming, which efficiently solves problems that require repeated decision-making or that involve uncertainty. It also works on social mathematics, which uses mathematical techniques to design fair systems and policies that people find acceptable.
MembersFaculty
- ProfessorHirokazu Anai
- ProfessorHayato Waki
- Associate ProfessorAkifumi Kira
- Associate ProfessorToshiaki Yachimura
- Assistant ProfessorGeunsu Kim
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Undirected NetworkX Graph” KalebD07 / CC0 (cropped)
- Solving Problems with Mathematical Techniques and Artificial Intelligence: “Problem Solving - Concept Illustration” Digits.co.uk Images / CC BY 2.0 (cropped)
- Optimization Problems Involving Continuous Variables: “Meta-Optimization Concept” Pedersen, M.E.H., Tuning & Simplifying Heuristical Optimization, PhD Thesis, 2010, University of Southampton, School of Engineering Sciences, Computational Engineering and Design Group. / Public domain (cropped)
- Dynamic Programming and Social Mathematics: “Decision Tree Anatomy” Lapollard / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory Lab): “Set Estimation from Reflected Brownian Motion 02” MGromov / CC BY-SA 4.0 (cropped)
- Related lab (Mathematical Physics Lab): “Crabbers eye knot-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (Mathematical Biology Lab): “SaintpauliaLeaf-7” Kārlis Kalviškis / CC BY-SA 4.0 (cropped)
- Related lab (Computational Mathematics Lab): “Level set method” Nicoguaro / CC BY 4.0 (cropped)
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