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Mathematical Optimization Lab
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The lab backs the idea that "optimization is the key to problem solving" with solid theory.
AboutAbout the lab
Optimization: the key to problem solving.
The Mathematical Optimization Lab studies the theory and applications of mathematical optimization.
Mathematical optimization means turning a wide range of social problems into mathematical models, finding solutions with algorithms suited to those models, and putting those solutions into practice as solutions to the problems.
The lab's basic policy is to conduct theory-focused research while keeping a firm eye on applications to real-world problems.
Key terms
- Mathematical optimization
- Mathematically finding, among the solutions that satisfy given conditions, the one that makes an objective value the smallest (or largest)
- Robust optimization
- A method in which a range of uncertainty is specified in advance, and the solution is optimized so that it still holds up even if the worst case within that range occurs
- Equilibrium problem
- A problem of finding the state (equilibrium) that multiple decision makers settle into when each acts optimally
NewsLab news
A doctoral student received the Student Outstanding Presentation Award at the Operations Research Society of Japan 2026 Autumn Research Presentation Conference
Assistant Professor Shotaro Yagishita received the Best Author Award (Paper category) from the Japan Society for Industrial and Applied Mathematics
A graduate's master's thesis received the FY2026 Student Paper Award from the Operations Research Society of Japan
Associate Professor Ellen Hidemi Fukuda was elected a Fellow of the Operations Research Society of Japan
ResearchResearch themes
Under the motto "Optimization is the key to problem solving," the lab studies modeling methods for optimization problems, the clarification of the theoretical properties of those problems, and the development of solution methods (algorithms). It aims to provide practical problem-solving methods that span engineering, management, and finance.
*Illustrative imageOptimization that withstands uncertainty
To handle uncertainty such as future demand and costs, the lab studies stochastic optimization, which treats uncertainty as probabilistic events, and robust optimization, which optimizes against the worst case.
*Illustrative imageFinding an equilibrium that everyone settles into
These are problems with multiple decision makers who each try to optimize, and the goal is to find the equilibrium state that results when each acts optimally. They arise in games as well as in economics, transportation engineering, and financial engineering.
*Illustrative imageBilevel optimization and MPEC
The lab studies optimization problems with two levels, upper and lower, such as when a leader optimizes while predicting the follower's response, as well as optimization problems that include equilibrium conditions as constraints (mathematical programs with equilibrium constraints, or MPEC).
*Illustrative imageApplications to finance and transportation
The lab has applied mathematical optimization to portfolio optimization, which raises returns while limiting risk; to traffic equilibrium problems, which predict the routes drivers choose on roads; and to data mining and communications engineering.
MembersFaculty
Members of the Mathematical Optimization Lab include faculty, doctoral students, and master's students.
- ProfessorNobuo Yamashita
- Associate ProfessorEllen Hidemi Fukuda
- Assistant ProfessorShotaro Yagishita
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: “Gradient ascent (surface)” 作者不詳 / Public domain (cropped)
- Optimization that withstands uncertainty: “SIDD inventory monitoring camera system in storage environment” Adapta Robotics / CC BY-SA 4.0 (cropped)
- Finding an equilibrium that everyone settles into: “Paris - Playing chess at the Jardins du Luxembourg - 2966” Jorge Royan / CC BY-SA 3.0 (cropped)
- Bilevel optimization and MPEC: “Decision Tree Depth 2” CollaborativeGeneticist / CC BY-SA 4.0 (cropped)
- Applications to finance and transportation: “Traffic Jam on the M62 - geograph.org.uk - 7390393” Chris Heaton / CC BY-SA 2.0 (cropped)
- Related lab (Statistical Intelligence Lab): “Normal distribution function” Shishirdasika / CC BY-SA 3.0 (cropped)
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- Related lab (Computer Software Lab): “Source code in Javascript” Romainhk / CC BY-SA 3.0 (cropped)
- Related lab (Intelligent Computing Lab): “Water Dolphin” JJ Harrison (https://www.jjharrison.com.au/) / CC BY-SA 3.0 (cropped)
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