Seminar: Indefinite Stiefel manifold: first-order geometry and Riemannian optimization

Time:

Venue/Location: Phòng C101, VIASM

Báo cáo viên: ThS. Đinh Văn Tiệp (Trường ĐH Kỹ thuật Công nghiệp, ĐH Thái Nguyên)

Tóm tắt: We consider the optimization problem with a quadratic matrix constraint whose feasible set constitutes a differentiable manifold, called the indefinite Stiefel manifold. We approach this problem within the framework of Riemannian optimization. Namely, we first equip the manifold with a Riemannian metric and construct the associated geometric structures, then propose a retraction based on the Cayley transform, and finally suggest a Riemannian gradient descent method using the attained materials, whose global convergence is guaranteed. Our results not only cover the known cases, the orthogonal and generalized Stiefel manifolds, but also provide a Riemannian optimization solution for other constrained problems which has not been investigated. Numerical experiments are presented to justify the theoretical findings