SpeedMapping.jl: Implementing Alternating cyclic extrapolations
2021-07-28, 17:50–18:00 (UTC), Red

SpeedMapping.jl implements Alternating cyclic extrapolations: a new and fast algorithm for accelerating optimization algorithms. It may be used for a large class of problems requiring a solution to the mapping F(x) = x. It also performs multivariate optimization often faster than L-BFGS or the nonlinear conjugate gradient method, especially with box-constraints. It will be useful in statistics, computer science, physics, biology or economics and many other fields.

The talk will briefly explain the ideas behind the method and demonstrate its use with two examples: i) computing a dominant eigenvalue by accelerating the power iteration ii) minimizing a multivariate Rosenbrock function with or without constraint by providing only the objective or only the gradient. Benchmarks will show significant speed gains over the L-BFGS and the nonlinear conjugate gradient.

A notebook for the talk may be downloaded at https://github.com/NicolasL-S/SpeedMapping.jl/blob/main/Resources/SpeedMapping_JuliaCon2021.ipynb

SpeedMapping may be installed directly from the REPL, or downloaded here: https://github.com/NicolasL-S/SpeedMapping.jl

The Alternating cyclic extrapolation method is detailed in:

N. Lepage-Saucier, Alternating cyclic extrapolation methods for optimization algorithms, arXiv:2104.04974 (2021). https://arxiv.org/abs/2104.04974

The paper also shows other applications, such as a logistic regression, a large set of CUTEst unconstrained problems, accelerating the expectation-maximization (EM) algorithm for Poisson mixtures and for a proportional hazards regression with interval censoring, for canonical tensor decomposition, and for the method of alternating projections (MAP) applied to regressions with high-dimensional fixed effects.

Economist living in Montreal. I'm interested in numerical methods and scarred for life by the experience of waiting six months for my estimates to converge.