Adaptive cubic regularization methods have emerged as a credible alternative to linesearch
and trust-region for smooth nonconvex optimization, with optimal complexity amongst …

We present a stochastic optimization method that uses a fourth-order regularized model to
find local minima of smooth and potentially non-convex objective functions with a finite-sum …

High-order tensor methods that employ Taylor-based local models (of degree p≥ 3) within
adaptive regularization frameworks have been recently proposed for both convex and …

Given a twice-continuously differentiable vector-valued function r (x), a local minimizer of ‖ r
(x) ‖ _2‖ r (x)‖ 2 is sought. We propose and analyse tensor-Newton methods, in which r …

A significant theoretical advantage of high-order optimization methods is their superior
convergence guarantees. For instance, third-order regularized methods reach an third-order …

High-order tensor methods that employ Taylor-based local models (of degree $ p\ge 3$)
within adaptive regularization frameworks have been recently proposed for both convex and …

Optimization problems constrained by partial differential equations (PDEs) naturally arise in
scientific computing, as those constraints often model physical systems or the simulation …

Use of second-order sensitivity information has been shown in the literature to yield faster
convergence, better noise tolerance, and localization besides enhanced post-reconstruction …

The aim of the article is to refer the use of regression analysis to estimate the parameters of
selected parametric mortality models, known as mortality laws. We are looking at mortality …

In this work, we set up the use of a Tensor-Newton scheme for solving the nonlinear
reconstruction problem for the fluorophore absorption coefficient, μaf x in SPN modeled …