A three-parameter scaled memoryless BFGS method for parameter estimation and its applications

The parameter estimation problem is inevitable and necessary to address in numerous scientific domains. In this paper, we present a three-parameter scaled memoryless BFGS method applicable for solving the parameter estimation problem. This method enhances the efficiency and robustness of the algorithm through three adaptive parameters. Furthermore, a methodology for parameter selection is provided. Under reasonable conditions, the global convergence of the new algorithm is demonstrated. To validate the efficiency and robustness of the algorithm, a substantial number of academic problems originating from the real world are employed for numerical experiments. Moreover, two real-world problems, the Muskingum model and a machine learning problem, are also utilized to verify the effectiveness and practicability of the algorithm. The results of these experiments indicate that the newly proposed method in this paper is effective and robust and can be widely utilized.