A restart derivative-free algorithm for solving pseudomonotone equations

In this work, we propose an efficient derivative-free algorithm strengthened by a restart strategy for solving nonlinear pseudomonotone equations. We have shown that the algorithm’s direction of search is descent and bounded and that the algorithm generates globally convergent sequences to the solutions under the assumptions of pseudomonotonicity and continuity. Moreover, the behavior of the convergent sequence near its limit is revealed for which we have shown that the sequence approaches its limit along the direction in the normal cone at the limit when the solution is not unique. Numerical simulations on benchmark test problems reveal the computational efficiency of our proposed algorithm in comparison with some existing recent ones. The suitability of the suggested algorithm for logistic regression problems is demonstrated, as well.