Abstract An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to …
Abstract An Adaptive Regularisation framework using Cubics (ARC) was proposed for unconstrained optimization and analysed in Cartis, Gould and Toint (Part I, Math Program …
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 …
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order …
The simulation of crack initiation and propagation in an elastic material is difficult, as crack paths with complex topologies have to be resolved. Phase-field approaches allow to …
LN Vicente - EURO Journal on Computational Optimization, 2013 - Springer
In this paper, we prove that the broad class of direct-search methods of directional type based on imposing sufficient decrease to accept new iterates shares the worst case …
C Cartis, NIM Gould, PL Toint - IMA Journal of Numerical …, 2012 - ieeexplore.ieee.org
The adaptive cubic regularization algorithm described in Cartis et al.(2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and …
Y Liu, F Roosta - arXiv preprint arXiv:2208.07095, 2022 - arxiv.org
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 …
JC Ziems, S Ulbrich - SIAM Journal on Optimization, 2011 - SIAM
We present a class of inexact adaptive multilevel trust-region SQP methods for the efficient solution of optimization problems governed by nonlinear PDEs. The algorithm starts with a …