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math.OC2022★ 2 cited
A Newton-MR algorithm with complexity guarantees for nonconvex smooth unconstrained optimization
Yang Liu, Fred Roosta
In this paper, we consider variants of Newton-MR algorithm for solving unconstrained, smooth, but non-convex optimization problems. Unlike the overwhelming majority of Newton-type…
math.OC2022
MINRES: From Negative Curvature Detection to Monotonicity Properties
Yang Liu, Fred Roosta
The conjugate gradient method (CG) has long been the workhorse for inner-iterations of second-order algorithms for large-scale nonconvex optimization. Prominent examples include li…