Do you know the difference between an optimist and a pessimist? The former believes we
live in the best possible world, and the latter is afraid that the former might be right.… In that …

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex
equality constrained optimization when a nearly feasible point is known. In particular, we first …

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 …

There has been growing interest in high-order tensor methods for nonconvex optimization,
with adaptive regularization, as they possess better/optimal worst-case evaluation …

Despite their popularity in the field of continuous optimisation, second-order quasi-Newton
methods are challenging to apply in machine learning, as the Hessian matrix is intractably …

Nonlinear conjugate gradients are among the most popular techniques for solving
continuous optimization problems. Although these schemes have long been studied from a …

A class of second-order algorithms is proposed for minimizing smooth nonconvex functions
that alternates between regularized Newton and negative curvature steps in an iteration …

The difficulty of minimizing a nonconvex function is in part explained by the presence of
saddle points. This slows down optimization algorithms and impacts worst-case complexity …

The conjugate gradient method (CG) has long been the workhorse for inner-iterations of
second-order algorithms for large-scale nonconvex optimization. Prominent examples …

We consider variants of a recently developed Newton-CG algorithm for nonconvex problems
(Royer, CW & Wright, SJ (2018) Complexity analysis of second-order line-search algorithms …