In this paper we develop new tensor methods for unconstrained convex optimization, which
solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial …

We present a Newton-type method that converges fast from any initialization and for arbitrary
convex objectives with Lipschitz Hessians. We achieve this by merging the ideas of cubic …

Motivated by recent increased interest in optimization algorithms for non-convex
optimization in application to training deep neural networks and other optimization problems …

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 …

This paper settles an open and challenging question pertaining to the design of simple and
optimal high-order methods for solving smooth and monotone variational inequalities (VIs) …

In this paper, we study p-order methods for unconstrained minimization of convex functions
that are p-times differentiable (p≧2) with ν-Hölder continuous p th derivatives. We propose …

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization
problems with general inexpensive constraints, ie, problems where the cost of …

We establish or refute the optimality of inexact second-order methods for unconstrained
nonconvex optimization from the point of view of worst-case evaluation complexity …

In this paper we study the worst-case complexity of an inexact augmented Lagrangian
method for nonconvex constrained problems. Assuming that the penalty parameters are …

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a
convex function in a finite-dimensional Euclidean space. Given a function\varPhi: R^ d → R …