Abstract
In this study, a new adaptive trust-region strategy is presented to solve nonlinear systems. More specifically, we propose a new method leading to produce a smaller trust-region radius close to the optimizer and a larger trust-region radius far away from the optimizer. Accordingly, it can lead to a smaller step-size close to the optimizer and a larger one far away from the optimizer. The new strategy includes a convex combination of the maximum norm of function value of some preceding successful iterates and the current norm of function value. The global convergence of the proposed approach is established while the local q-quadratic convergence rate is proved under local error bound condition, which is weaker than the nonsingularity. Numerical results of the proposed algorithm are also reported.
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Esmaeili, H., Kimiaei, M. A trust-region method with improved adaptive radius for systems of nonlinear equations. Math Meth Oper Res 83, 109–125 (2016). https://doi.org/10.1007/s00186-015-0522-0
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DOI: https://doi.org/10.1007/s00186-015-0522-0