Quasi-Newton trust region algorithm for non-smooth least squares problems

In this paper we present a quasi-Newton trust region algorithm for non-smooth least squares problems which possess the smooth plus non-smooth decomposition. This method uses a smooth subproblem with second order information to approximate the locally Lipschitzian function, which is important to increase the convergence rate of the algorithm and deal with the large-residual non-smooth least squares problems. The global and superlinear convergence of this algorithm are established.

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