Research Topics
Main research interests include solution methods for decision making problems under uncertainty, large-scale optimization problems and nonconvex optimization problems, which appear in operations research, machine learning, control, etc. We develop models and algorithms for solving those problems, and examine the computational efficiency of the proposed methods.
In recent years, I'm working on the following research topics. For more details, see research results in FY2018 and FY2019 (in Japanese, sorry).
Nonconvex Optimization
It is difficult to find global optima for general nonconvex optimization problems. I have studied these topics, e.g.,
- what kind of nonconvex optimization problems can be solved globally by polynomial-time optimization algorithms,
- how to efficiently find stationary points for nonconvex quadratic optimization problems / structured nonsmooth nonconvex optimization problems.
Optimization Methods in Machine Learning
In machine learning field, methods for finding hidden regularities from past data are developed, and they are used for prediction. Those methods are utilized in a wide range of applications such as medical diagnostics, spam mail detection, financial market prediction, and character recognition. During the process, mathematical optimization problems are often formulated and optimization techniques are applied. From the perspective of whether there is a better modeling or a better solution method, I would like to carry out research utilizing my knowledge of mathematical optimization.
Optimization Methods under Uncertainty
When making a power generation plan for an electronic power company or a production plan for a manufacturing company, methods considering the uncertainty of demand are required. Robust optimization methods are known as methods for making robust decision-making against uncertainty. We are conducting research from a theoretical perspective in order to broaden the scope of application of the robust optimization method.