Graduate School of
Science and Engineering

Optimization, a branch of applied mathematics, has important applications in machine learning, control engineering, financial engineering, and other fields. I have been studying geometric optimization on Riemannian manifolds, where constrained optimization problems in the Euclidean space or more abstract problems are considered unconstrained optimization problems on manifolds, such as the Stiefel and Grassmann manifolds. Given the interdisciplinary nature of this research field and its diverse applications, I collaborate with researchers in various fields, including control engineering, numerical linear algebra, and statistics. My recent interests include general theories of Riemannian optimization methods such as the conjugate gradient and Newton-like methods, as well as applications of Riemannian optimization to other fields such as control engineering and numerical linear algebra. In my research, I typically propose novel and effective algorithms and mathematically analyzes them, proving, for example, the global convergence of the proposed algorithms.