Abstract
In this paper, we have presented a numerical algorithm for the step-size estimation for minimization problems. Global convergence results are derived for descent algorithms in which the line search step is replaced by a step whose length is determined by step-size estimation formula. Numerical results show that the new estimation step-size required less storage and greatly speeded up the convergence of the gradient algorithm for large-scale unconstrained optimization problems. Also the new proposed algorithm seems to converge better and superior to other similar algorithms in many situations.