Summary: Memoryless quasi-Newton methods are studied for solving largescale unconstrained optimization problems. In earlier work, the author proposed a memoryless quasi-Newton method based on the spectral-scaling Broyden family and showed that the method satisfies the sufficient descent condition and converges globally. To relax the conditions on parameters in the method, we apply the modification technique by C. X. Kou and Y. H. Dai [J. Optim. Theory Appl. 165, No. 1, 209–224 (2015; Zbl 1319.49042)] to the method of Nakayama et al., and we give a hybrid method of the three-term conjugate gradient method and the memoryless quasi-Newton method based on the spectral-scaling Broyden family. We show that our method satisfies the sufficient descent condition, and we prove that the method converges globally.
Furthermore, we give a concrete choice of parameters for our method. Finally, some numerical results are given.