An efficient double inertial-type derivative-free sufficient descent algorithm to solve nonlinear equations

Abstract

To enhance the performance of iterative algorithms, recent studies have emphasised the use of double inertial extrapolation steps. This work proposes a family of sufficient descent iterative algorithms incorporating a double inertial extrapolation strategy for solving nonlinear equations. Global convergence of the proposed methods is established under mild assumptions. Specifically, the global convergence is achieved without requiring Lipschitz continuity and assuming only generalised monotonicity, which is weaker than pseudo-monotonicity. In addition, under the local Lipschitz continuity assumption, we establish the asymptotic and non-asymptotic convergence rates in terms of iteration complexity. To the best of our knowledge, this work is the first to establish both asymptotic and non-asymptotic convergence rates for a derivative-free method under a double inertial framework. Furthermore, numerical experiments confirm the effectiveness and robustness of the proposed algorithms when compared with the recent inertial-based methods on standard test problems. Moreover, their applicability to regularised decentralised logistic regression and sparse signal restoration problems is demonstrated. � The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2026.