Volume 1, Issue 1
An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations

T. Sogabe, A. Suzuki & S.-L. Zhang

CSIAM Trans. Appl. Math., 1 (2020), pp. 142-154.

Published online: 2020-03

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  • 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.

  • Keywords

Shifted linear systems, symmetric positive definite, the shifted conjugate gradient method, sphere constrained quadratic optimizations, Ye’s hybrid method.

  • AMS Subject Headings

65F10, 65K05, 90C20

  • Copyright

COPYRIGHT: © Global Science Press

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  • RIS
  • TXT
@Article{CSIAM-AM-1-142, author = {Sogabe , T. and Suzuki , A. and Zhang , S.-L. }, title = {An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {1}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0008}, url = {http://global-sci.org/intro/article_detail/csiam-am/16796.html} }
TY - JOUR T1 - An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations AU - Sogabe , T. AU - Suzuki , A. AU - Zhang , S.-L. JO - CSIAM Transactions on Applied Mathematics VL - 1 SP - 142 EP - 154 PY - 2020 DA - 2020/03 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0008 UR - https://global-sci.org/intro/article_detail/csiam-am/16796.html KW - Shifted linear systems, symmetric positive definite, the shifted conjugate gradient method, sphere constrained quadratic optimizations, Ye’s hybrid method. AB -

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.

T. Sogabe, A. Suzuki & S.-L. Zhang. (2020). An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations. CSIAM Transactions on Applied Mathematics. 1 (1). 142-154. doi:10.4208/csiam-am.2020-0008
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