Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Zaiwen Wen,Peking University
Inviter:
周爱辉
Title:
Regularized Newton Type Methods for Riemannian Optimization
Time & Venue:
2018.9.20 10:00-11:00 N702
Abstract:
Optimization on Riemannian manifold widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low ranknearest correlation, etc. We propose an adaptive regularized NewtonType method which approximates the original objective function by the second-order Taylor expansion in Euclidean space but keeps the Riemannian manifold constraints. In particular, we are interested in applications that the Euclidean Hessian consists of acomputational cheap part and a significantly expensive part. Our basic idea is to keep these parts of lower computational costs but substitute those parts of higher computational costs by the limited-memory quasi-Newton update. The initial quasi-Newton matrix is further constructed from a limited-memory Nystrom approximation to the expensive part. Both global convergence and superlinear local convergence rate are guaranteed under mild conditions. Our algorithm is very promising in extensive experiments compared with a few state-of-art methods.