A New Modified TR Algorithm with Adaptive Radius to Solve a Nonlinear Systems of Equations

Abstract

The trust region method (TRM) is a very important technique to solve both of linear and nonlinear systems of equations. In this work, a new modified algorithm of a TRM with adaptive radius is introduced in purpose of solving systems of nonlinear equations. At each iteration, the new algorithm changes the trust region radius (TRR) automatically to reduce the subproblems resolving number when the current radius is rejected. The global convergence results of the new procedure under some appropriate conditions is established. The numerical effects indicate that the suggested algorithm is interesting and robustness.