no code implementations • 1 Aug 2023 • Ph. L. Toint
A very simple unidimensional function with Lipschitz continuous gradient is constructed such that the ADAM algorithm with constant stepsize, started from the origin, diverges when applied to minimize this function in the absence of noise on the gradient.
no code implementations • 14 Feb 2023 • S. Gratton, A. Kopanicakova, Ph. L. Toint
The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to noise, while the multi-level feature aims at reducing their computational cost.
no code implementations • 2 Nov 2020 • C. Cartis, N. I. M. Gould, Ph. L. Toint
A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems.
Optimization and Control 65Y20, 90C30, 90C60 F.2.1; G.1.6
no code implementations • 9 Dec 2018 • S. Gratton, Ph. L. Toint
This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control.
no code implementations • 9 Nov 2018 • S. Bellavia, G. Gurioli, B. Morini, Ph. L. Toint
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed.
