A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations (Q861492)

A new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus nonsmooth decomposition is presented. At each iteration, this method obtains a search direction not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. This approach may reduce computational effort and hence improve computational efficiency. It is also proved that under appropriate assumptions this algorithm is globally and locally superlinearly convergent. Some numerical examples are presented.