A limited memory BFGS (L-BFGS) algorithm is presented for solving large-scale symmetric nonlinear equations, where a line search technique without derivative information is used. The global convergence of the proposed algorithm is established under some suitable conditions. Numerical results show that the given method is competitive to those of the normal BFGS methods.
Xiangrong Li. Xiaoliang Wang. Xiabin Duan. "A Limited Memory BFGS Method for Solving Large-Scale Symmetric Nonlinear Equations." Abstr. Appl. Anal. 2014 (SI44) 1 - 9, 2014. https://doi.org/10.1155/2014/716019