7 papers
An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks
Joseph Webb, Sadok Jerad, Coralia Cartis
Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solv…
Fast Adaptive Tensor Methods Under Local Smoothness
Sadok Jerad
A new, fast adaptive regularization methods is proposed and analyzed under local Lipschitz smoothness of the -th order tensor. For nonconvex problems, it achieves the optimal $\…
A Parameter-Free First-Order Algorithm for Non-Convex Optimization with Global Rate
Sichao Xiong, Sadok Jerad, Coralia Cartis
We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve oracle complexity bound when minimizing sufficientl…
A Fast Newton Method Under Local Lipschitz Smoothness
Serge Gratton, Sadok Jerad, Philippe L. Toint
A new, fast second-order method is proposed that achieves the optimal complexity to obtain first-order -stationary points. Crucial…
On Global Rates for Regularization Methods based on Secant Derivative Approximations
Coralia Cartis, Sadok Jerad, Karl Welzel
An inexact and globally convergent framework for high-order adaptive regularization methods is presented, in which approximations may be used for the th-order tensor, based on l…
Complexity and performance for two classes of noise-tolerant first-order algorithms
S. Gratton, S. Jerad, Ph. L. Toint
Two classes of algorithms for optimization in the presence of noise are presented, that do not require the evaluation of the objective function. The first generalizes the well-know…