On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation
arXiv:1504.03442
Originality Synthesis-oriented
AI Analysis
It provides a theoretically grounded regularization strategy for ill-posed nonlinear problems, which is an incremental contribution to numerical optimization.
The paper proposes a trust-region method with an adaptive regularization parameter for solving nonlinear ill-posed systems, demonstrating theoretically and numerically that it can approach the solution of the unperturbed system.
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.