arXiv subjects

Nicolas Lepage-Saucier

Publications and source records attributed to Nicolas Lepage-Saucier.

2 recordsLinked to original sources

arXiv2024

Anderson acceleration with adaptive relaxation for convergent fixed-point iterations

Two adaptive relaxation strategies are proposed for Anderson acceleration. They are specifically designed for applications in which mappings converge to a fixed point. Their superiority over alternative Anderson acceleration is demonstrated for linear contraction mappings. Both strategies perform well in three nonlinear fixed-point applications that include partial differential equations and the EM algorithm. One strategy surpasses all other Anderson acceleration implementations tested in terms of computation time across various specifications, including composite Anderson acceleration.

math.NA↗

arXiv2021

Alternating cyclic extrapolation methods for optimization algorithms

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The methods require no problem-specific adaptation and are especially efficient in high-dimensional contexts. Their computation uses few objective function evaluations, no matrix inversion and little extra memory. A convergence analysis is followed by eight applications including gradient descent acceleration for constrained and unconstrained optimization. Performances are on par with or better than competitive alternatives. The algorithm is available as the Julia package SpeedMapping.jl.

math.OC↗