A class of relaxed-inertial derivative-free projection method beyond monotonicity with application

Recent advances have introduced derivative-free projection methods incorporating a relaxed-inertial technique to solve large-scale systems of nonlinear equations (LSoNE). These methods are often studied under restrictive assumptions such as monotonicity and Lipschitz continuity assumptions. In this paper, we propose a new class of derivative-free projection method with a relaxed inertial technique for solving LSoNE. Unlike existing approaches that rely on monotonicity and Lipschitz continuity assumptions, our method extends beyond these limitations, broadening the applicability of projection methods to more general problem classes. This enhances both the theoretical framework and the practical efficiency in large-scale applications. Moreover, we establish global convergence without the need for a summability condition on the inertial extrapolation step length. To demonstrate the effectiveness of the method, we present numerical experiments to solve LSoNE and regularized decentralized logistic regression, a key problem in machine learning applications.