Accelerated diagonal gradient-type method for large-scale unconstrained optimization

In this study, we propose an accelerated diagonal-updating scheme for solving large-scale optimization, where a scaled diagonal matrix is used to approximate the Hessian. We combine an accelerator with the diagonal-updating method to improve the efficiency of the algorithm. This accelerator is employed to ensure that the function value can be reduced significantly at each step. Moreover, the algorithm employs a suitable monotone strategy to guarantee the global convergence of the algorithm. Several numerical results are reported, which demonstrate that the proposed method is promising and more robust than other diagonal updating schemes.