Codes for "Regularisation, optimisation, subregularity"

This repository contains the codes for the numerical demonstrations in “Regularisation, optimisation, subregularity” (https://arxiv.org/abs/2011.07575).

Prerequisites

These codes were written for Julia 1.5.2. The package dependencies are from January 2021 when our experiments were run. You may get Julia from julialang.org.

Using

Navigate your unix shell to the directory containing this README.md and then run:

sh $ julia --project=.

The first time doing this, to ensure all the dependencies are installed, run

julia> ]instantiate

Afterwards in the Julia shell, type:

julia> using Regtheory

This may take a while as Julia precompiles the code. Then, to generate all the experiments in the manuscript, run:

julia> batchrun()

This will write the data in the manusript to tv-results.txt, and the images to several files of the form data_*.png, reco_*.png, and error_*.png. To alter the computations performed, see src/TV.jl. In particular, the array experiments_tv lists the different the parameters $α$, $δ$, and $N$ while default_params contains the parameters of the algorithm.