Web: http://arxiv.org/abs/1810.00303

May 9, 2022, 1:11 a.m. | Fred Roosta, Yang Liu, Peng Xu, Michael W. Mahoney

cs.LG updates on arXiv.org arxiv.org

We consider a variant of inexact Newton Method, called Newton-MR, in which
the least-squares sub-problems are solved approximately using Minimum Residual
method. By construction, Newton-MR can be readily applied for unconstrained
optimization of a class of non-convex problems known as invex, which subsumes
convexity as a sub-class. For invex optimization, instead of the classical
Lipschitz continuity assumptions on gradient and Hessian, Newton-MR's global
convergence can be guaranteed under a weaker notion of joint regularity of
Hessian and gradient. We also …

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