MODIFICATION OF THE ARMIJO LINE SEARCH TO SATISFY THE GLOBAL CONVERGENCE OF LIU-STOREY METHOD

In this paper, we propose a new Armijo-modified line search strategy that provides an efficient way to determine the step size at each iteration. The proposed modification ensures the global convergence of the original line search (LS) conjugate gradient method under some assumptions. By incorporating this modified line search, the algorithm benefits from stability when solving large-scale unconstrained optimization problems. To demonstrate the effectiveness of the proposed approach, we present a set of comprehensive numerical experiments. These tests compare the new scheme with existing classical line search techniques, highlighting its competitive performance in terms of accuracy, convergence speed, and computational efficiency. The results confirm that the proposed Armijo-modified line search is a valuable improvement to conjugate gradient methods.