Two Classes of Restart Algorithms for Solving Pseudomonotone Nonlinear Equations

Abstract

In this study, we introduce two efficient derivative-free algorithms enhanced by a restart strategy to solve nonlinear pseudomonotone equations. We demonstrate that the algorithm’s search direction is both descent and bounded, and under the assumptions of pseudomonotonicity and continuity, the algorithm generates globally convergent sequences toward the solutions. Numerical experiments on benchmark test problems highlight the computational efficiency of our proposed algorithm compared to several existing methods. Additionally, we illustrate the algorithm’s applicability to logistic regression problems, showcasing its practical relevance.