An Implicit Evaluation Method of Vector 2-Norms Arising from Sphere Constrained Quadratic Optimizations (CSIAM Transactions on Applied Mathematics, 2020)
An implicit evaluation method of vector 2-norms is presented for functionevaluations arising from sphere constrained quadratic optimizations. The efficiency ofthe method in terms of computational costs mainly comes from the well-known shiftedconjugate gradient method, and the robustness of the method comes from the fact thatit never suffers from cancellations when the coefficient matrix is symmetric positivedefinite. Numerical experiments indicates that the method is promising for reducingcomputational costs of Ye's hybrid method for solving sphere constrained quadraticoptimizations.