An adaptive nonmonotone line search technique for solving systems of nonlinear equations (Q2666440)

Summary: In this article, a new nonmonotone line search technique is proposed for solving a system of nonlinear equations. We attempt to answer this question how to control the degree of the nonmonotonicity of line search rules in order to reach a more efficient algorithm? Therefore, we present a novel algorithm that can avoid the increase of unsuccessful iterations. For this purpose, we show the robust behavior of the proposed algorithm by solving a few numerical examples. Under some suitable assumptions, the global convergence of our strategy is proved.