Academic Reports (On Friday)——Dense initialization for limited-memory quasi-Newton methods
主 题: Academic Reports (On Friday)——Dense initialization for limited-memory quasi-Newton methods
报告人: Professor Oleg Burdakov (Linkeoping University, Sweden )
时 间: 2017-11-24 15:00-16:00
地 点: Room 1114, Sciences Building No. 1
Abstract: We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization uses two parameters to approximate the curvature of the Hessian in two complementary subspaces. This family of dense initializations is proposed in the context of a limited-memory Broyden-Fletcher-Goldfarb-Shanno ({L-BFGS}) trust-region method that makes use of a shape-changing norm to define each subproblem. As with {L-BFGS} methods that traditionally use diagonal initialization, the dense initialization and the sequence of generated quasi-Newton matrices are never explicitly formed. Numerical experiments on the CUTEst test set suggest that this initialization together with the shape-changing trust-region method outperforms other L-BFGS methods for solving general nonconvex unconstrained optimization problems. While this dense initialization is proposed in the context of a special trust-region method, it has broad applications for more general quasi-Newton trust-region and line search methods. In fact, this initialization is suitable for use with any quasi-Newton update that admits a compact representation and, in particular, any member of the Broyden class of updates.
