An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations

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.