An Inexact Quasi-Newton Algorithm Combined with Jacobian Restart Technique for Nonlinear Equation Systems

Quasi-Newton methods are the efficient alternative to Newton methods for solving nonlinear equation systems, since it can overcome the troubles of mass computing or hard to compute for Jacobian matrices. An inexact Broyden rank one quasi-Newton algorithm is proposed in this paper. It can be guaranteed the search directions are descent directions for any norm of system of equations in new algorithm. Moreover, an inexact search technique is exploited such that some redundant steps can be left out and the demand for memory can be saved.