In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically.
On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation / Bellavia, Stefania; Morini, Benedetta; Riccietti, Elisa. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 64:(2016), pp. 1-30. [10.1007/s10589-015-9806-9]
On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation
BELLAVIA, STEFANIA;MORINI, BENEDETTA;RICCIETTI, ELISA
2016
Abstract
In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically.
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