Research

My research has focused on Riemannian optimization (optimization on Riemannian manifolds) theory and its applications. A constrained optimization problem whose feasible points form a Riemannian manifold can be reformulated as an unconstrained optimization problem on the manifold.

My research has particularly focused on generalizing conjugate gradient methods to Riemannian manifolds. Furthermore, many practical problems are formulated as optimization problems on Riemannian manifolds. I do not only study mathematical aspects of algorithms but also verify the proposed algorithms through numerical experiments and solving practical problems.

Recent Research Interests

• Generalization of nonlinear conjugate gradient methods to Riemannian manifolds and its analysis

• Generalization of stochastic optimization methods to Riemannian manifolds and its analysis

• Numerical linear algebra approach to Riemannian Newton's equation

• Applications of Riemannian optimization methods to a variety of fields such as numerical linear algebra, control theory, and statistics