A modification of steepest descent method for solving large-scaled unconstrained optimization problems

Abstract

In this paper, we develop a new search direction for Steepest Descent (SD) method by replacing previous search direction from Conjugate Gradient (CG) method, , with gradient from the previous step,  for solving large-scale optimization problem. We also used one of the conjugate coefficient as a coefficient for matrix . Under some reasonable assumptions, we prove that the proposed method with exact line search satisfies descent property and possesses the globally convergent. Further, the numerical results on some unconstrained optimization problem show that the proposed algorithm is promising.