A Simple Sufficient Descent Method for Unconstrained Optimization

We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed method converges globally. Numerical experiments on some unconstrained minimization problems from CUTEr library are reported, which illustrate that the proposed method is promising.