Nonconvex and nonsmooth optimization problems are frequently encountered in much of
statistics, business, science and engineering, but they are not yet widely recognized as a …

There has been much recent interest in finding unconstrained local minima of smooth
functions, due in part to the prevalence of such problems in machine learning and robust …

We consider minimization of a smooth nonconvex objective function using an iterative
algorithm based on Newton's method and the linear conjugate gradient algorithm, with …

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 propose a first second-order scheme based on arbitrary non-Euclidean
norms, incorporated by Bregman distances. They are introduced directly in the Newton …

In this paper, we study the problem of escaping from saddle points in smooth nonconvex
optimization problems subject to a convex set $\mathcal {C} $. We propose a generic …

In this paper, we study the regularized second-order methods for unconstrained
minimization of a twice-differentiable (convex or nonconvex) objective function. For the …

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 …

Worst-case complexity guarantees for nonconvex optimization algorithms have been a topic
of growing interest. Multiple frameworks that achieve the best known complexity bounds …

We propose a stochastic variance-reduced cubic regularized Newton method (SVRC) for
non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient …