A superlinearly convergent ODE-type trust region algorithm for nonsmooth nonlinear equations
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This paper presents a new trust region algorithm for solving nonsmooth nonlinear equation problems which posses the smooth plus non-smooth decomposition. At each iteration, this method obtains a trial step by solving a system of linear equations, hence avoiding the need for solving a quadratic programming subproblem with a trust region bound. From a computational point of view, this approach may reduce computational effort and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and locally super-linearly convergent. Some numerical examples are reported.
AMS Mathematics Subject Classification90C30 65K05
Key words and phrasesNonsmooth nonlinear equations ODE methods trust region methods superlinear convergence
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