A New Adaptive Accelerated Levenberg–Marquardt Method for Solving Nonlinear Equations and Its Applications in Supply Chain Problems

Abstract

In this paper, a new adaptive Levenberg–Marquardt method is proposed to solve the nonlinear equations including supply chain optimization problems. We present a new adaptive update rule which is a segmented function on the ratio between the actual and predicted reductions of the objective function to accept a large number of unsuccessful iterations and avoid jumping in local areas. The global convergence and quadratic convergence of the proposed method are proved by using the trust region technique and local error bound condition, respectively. In addition, we use the proposed algorithm to test on the symmetric and asymmetric linear equations. Numerical results show that the proposed method has good numerical performance and development prospects. Furthermore, we apply the algorithm to solve the fresh agricultural products supply chain optimization problems.