Global convergence of a spectral conjugate gradient method for unconstrained optimization
Summary: A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition \(g^T_k d_k < -||g_k||^2\). Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library [\textit{I. Bongartz, A. R. Conn, N. Gould} and \textit{P. L. Toint}, ACM Trans. Math. Softw. 21, No. 1, 123--160 (1995; Zbl 0886.65058)] in contrast to the famous CD method, FR method, and PRP method.
scientific article; zbMATH DE number 6078801
scientific article