A new super-memory gradient method with curve search rule

In this paper, we propose a new super-memory gradient method with curve search rule for unconstrained optimization problems. The method uses previous multi-step iterative information and some curve search rules to generate new iterative points at each iteration. This makes the new method converge stably and be more suitable for solving large scale optimization problems than other similar methods. We analyze the global convergence and convergence rate under some mild conditions. Numerical experiments show that some new algorithms are available and effective in practical computation.