A Levenberg–Marquardt type algorithm with a Broyden-like update technique for solving nonlinear equations

Abstract

We propose a variant Broyden-like method for solving nonlinear equations. At each iteration, the proposed method solves a Levenberg–Marquardt type equation in which the matrix is updated by the Broyden-like formula. The global convergence ensured by a nonmonotone derivative-free line search is proved without the nonsingularity condition. Moreover, the proposed method has local quadratic convergence under suitable conditions. Numerical experiments show that our method is more effective than the traditional Broyden-like method.