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

Abstract

In this paper, we propose a new Armijo-modified line search strategy that pro-vides an ecient way to determine the step size at each iteration. The proposed modification ensures the global convergence of the original line search (LS) conjugate gradient methodunder some assumptions. By incorporating this modified line search, the algorithm benefits from stability when solving large-scale unconstrained optimization problems. To demonstratethe 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 com-putational eciency. The results confirm that the proposed Armijo-modified line search isa valuable improvement to conjugate gradient methods.