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An adaptive trust region algorithm for large-residual nonsmooth least squares problems

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  • In this paper, an adaptive trust region algorithm in which the trust region radius converges to zero is presented for solving large-residual nonsmooth least squares problems. This algorithm uses the smoothing technique of the approximation function, and it combines an adaptive trust region radius. Moreover, this algorithm differs from the existing methods for solving nonsmooth equations through use of the approximation function of second-order information, which improves the convergence rate for large-residual nonsmooth least squares problems. Under some suitable conditions, the global and local superlinear convergences of the proposed method are proven. The preliminary numerical results indicate that the proposed algorithm is effective and suitable for solving large-residual nonsmooth least squares problems.

    Mathematics Subject Classification: 90C26.

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  • Figure 1.  The value of $\|F(x_k)\|$ with iteration $k$ for Example 5.1

    Figure 2.  The value of $\|F(x_k)\|$ with iteration $k$ for Example 5.2

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