3 accepted papers
Second-order methods for convex optimization outperform first-order methods in terms of theoretical iteration convergence, achieving rates up to $O(k^{-5})$ for highly-smooth functions. However, their practical performance and applications are limited due to their multi-level structure and implement…
Computing homotopy groups of spheres has long been a fundamental objective in algebraic topology. Various theoretical and algorithmic approaches have been developed to tackle this problem. In this paper we take a step towards the goal of comprehending the group-theoretic structure of the generators…
In this paper, we present the first stepsize schedule for Newton method resulting in fast global and local convergence guarantees. In particular, we a) prove an $\mathcal O \left( 1/{k^2} \right)$ global rate, which matches the state-of-the-art global rate of cubically regularized Newton method of P…