RLS_Example.jl

This repo has the Julia code for the example in the paper

Robust solutions of nonlinear least squares problems via min-max optimization

by Xiaojun Chen and C. T. Kelley

You must know enough about Julia and GitHub to

• Use the package manager
• Know where to put projects so you can get to them with using XXX
• Clone a GitHub repo.

This repo is a Julia project RLS_Example.jl . The codes in this project produce the tables and figures in the paper. To get started

• Install the packages: LaTeXStrings, Optimization, OptimizationOptimJL, Polynomials, Printf, PyPlot, Zygote

• Clone this repo as RLS_Example.jl and either

  • store it as a subdirectory of any directory in your DEPOT_PATH (optimal choice)
  • cd to the src subdirectory of RLS_Example.jl and run it from in there

• Start Julia and type using RLS_Example at the Julia prompt

To make the tables type tables() at the Julia prompt.

To make the figures type figures() at the Julia prompt.

Nothing in this repo pretends to be a general purpose project and its only mission is to make the figures/tables for the paper.

Here is an example of how one would use the code to print the tables.

`` _ _ _(_)_ | Documentation: https://docs.julialang.org (_) | (_) (_) | _ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help. | | | | | | |/ _ | | | | || | | | (| | | Version 1.11.2 (2024-12-01) / |_'|||_'| | Official https://julialang.org/ release |_/ |

julia> using RLSExample [ Info: Precompiling RLSExample [9d6a3767-96d8-5986-83e8-8cac8e739f00]

julia> tables() Table 1 \begin{tabular}{llll} $\lambda$ &$\Psi\lambda$ &$| \nabla \Psi\lambda |$ & slope \ \hline 0.00e+00 & 2.21e-02 & 1.14e-12 & 0.00e+00 \ 1.00e-01 & 8.30e-01 & 2.27e-12 & 7.27e-01 \ 1.00e+00 & 5.05e+00 & 2.49e-11 & 6.15e+00 \ 5.00e+00 & 7.72e+00 & 2.44e-09 & 8.16e+00 \ 1.00e+01 & 8.85e+00 & 6.24e-10 & 8.27e+00 \ 1.00e+02 & 1.25e+01 & 5.69e-08 & 8.44e+00 \ \hline \end{tabular} Table 2 \begin{tabular}{llll} $\lambda$ &$\Psi\lambda$ &$| \nabla \Psi\lambda |$ & slope \ \hline 0.00e+00 & 4.51e-02 & 9.76e-16 & 0.00e+00 \ 1.00e+00 & 8.08e+00 & 2.91e-08 & 7.95e+00 \ 5.00e-01 & 5.05e+00 & 1.45e-10 & 3.98e+00 \ 1.00e+01 & 1.80e+01 & 2.60e-08 & 1.15e+01 \ 1.00e+02 & 3.62e+01 & 5.54e-08 & 1.19e+01 \ 2.00e+02 & 4.06e+01 & 5.23e-08 & 1.20e+01 \ \hline \end{tabular} Table 3 \begin{tabular}{llll} $\lambda$ &$\Psi\lambda$ &$| \nabla \Psi\lambda |$ & slope \ \hline 0.00e+00 & 4.51e-02 & 9.76e-16 & 0.00e+00 \ 1.00e+00 & 8.08e+00 & 2.91e-08 & 9.01e+00 \ 5.00e-01 & 5.05e+00 & 1.45e-10 & 4.36e+00 \ 1.00e+01 & 1.80e+01 & 2.60e-08 & 6.30e+01 \ 1.00e+02 & 3.62e+01 & 5.54e-08 & 9.86e+01 \ 2.00e+02 & 4.06e+01 & 5.23e-08 & 9.86e+01 \ \hline \end{tabular}

```