# Newton-type methods for non-convex optimization under inexact Hessian information

@article{Xu2017NewtontypeMF,
title={Newton-type methods for non-convex optimization under inexact Hessian information},
author={Peng Xu and Farbod Roosta-Khorasani and Michael W. Mahoney},
journal={Mathematical Programming},
year={2017},
pages={1-36}
}
• Published 23 August 2017
• Computer Science, Mathematics
• Mathematical Programming
We consider variants of trust-region and adaptive cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under certain condition on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve $$\varepsilon$$ε-approximate second-order optimality which have been shown to be tight. Our Hessian approximation condition offers a range of advantages as compared with the prior works…
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