An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations
Year: 2020
Author: T. Sogabe, A. Suzuki, S.-L. Zhang
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 142–154
Abstract
An implicit evaluation method of vector 2-norms is presented for function evaluations arising from sphere constrained quadratic optimizations. The efficiency of the method in terms of computational costs mainly comes from the well-known shifted conjugate gradient method, and the robustness of the method comes from the fact that it never suffers from cancellations when the coefficient matrix is symmetric positive definite. Numerical experiments indicates that the method is promising for reducing computational costs of Ye's hybrid method for solving sphere constrained quadratic optimizations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0008
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 142–154
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Shifted linear systems symmetric positive definite the shifted conjugate gradient method sphere constrained quadratic optimizations Ye’s hybrid method.