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Dense Initializations for Limited-Memory Quasi-Newton Methods. (arXiv:1710.02396v2 [math.OC] UPDATED)
来源于:arXiv
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 li 查看全文>>