Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

Authors:
Jinyan Fan
Affiliations:
Aff1 Aff2
Venue:
Computational Optimization and Applications
Year:
2006

Citing 2
Cited 1

Testing Unconstrained Optimization Software

ACM Transactions on Mathematical Software (TOMS)
On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption

Computing

An improved trust region algorithm for nonlinear equations

Computational Optimization and Applications

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Abstract

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given.