Relaxed-inertial derivative-free algorithm for systems of nonlinear pseudo-monotone equations

Solving systems of nonlinear equations has evolved into an active research field, with numerous iterative methods being proposed. Notably, iterative methods characterized by fast convergence remain of interest. In this paper, based on the modified line search scheme by Ou and Li, we introduce a derivative-free algorithm with a relaxed-inertial technique for approximating solutions of nonlinear systems involving pseudo-monotone mappings in Euclidean space. The global convergence of the proposed algorithm is established without Lipschitz continuity of the underlying mapping. Moreover, our approach allows flexibility in selecting the inertial extrapolation step length within the interval [0, 1]. To show the efficiency of the proposed method, we embed a derivative-free search direction into the scheme. Numerical experiments are given to illustrate the efficiency of the proposed algorithm for large-scale systems and sparse signal reconstruction.