A new parameter-free continuously differentiable filled function algorithm for solving nonlinear equations and data fitting problems

Filled function method, as an efficient method for finding the global minimizer of multimodal functions. It uses alternately classical optimization methods to minimize the objective function and the filled function until the global minimizer of the objective function is obtained. However, many efficient optimization methods based on gradient information cannot be used to minimize the filled function, which is not continuously differentiable. In addition, filled functions often contain parameters that are difficult to adjust. In this paper, a parameter- free continuously differentiable filled function without exponential terms or logarithmic terms and the corresponding filled function algorithm are proposed to overcome these shortcomings. Theoretical analysis and numerical verification show that our algorithm is feasible and effective. Furthermore, the algorithm is applied to solve nonlinear equations and data fitting problems. The numerical results prove the effectiveness of our algorithm. Finally, the advantages and disadvantages of our algorithm are analyzed, and the further research direction is discussed.