CRM-CFP

CRM to solve the Convex Feasibility Problem

This code base is using the Julia Language and DrWatson to make a reproducible scientific project named

CRM-CFP

CRM-CFP concerns numerical results presented in [Behling2021], [Arefidamghani2021], [Araujo2022], [Arefidamghani2023], [Behling2023a] [Behling2023b], and [Behling2023c], where the Circumcentered-Reflection Method (CRM) was used to solve the Convex Feasibility Problem (CFP) of finding a common point to the nonempty intersection of closed and convex sets.

It is authored by Luiz-Rafael Santos in co-authorship with Guilherme Araújo, Reza Arefidamghani, Roger Behling, Yunier Bello-Cruz and Alfredo N. Iusem.

How to use CRM-CFP

To (locally) reproduce this project, do the following:

0. Clone the repository locally

1. Open a Julia console and do:

   julia> using Pkg
   julia> Pkg.activate("path/to/this/project")
   julia> Pkg.instantiate()

   The last line is mandatory so julia install all packages. It is recommended that you build the packages in order to get the files running. For that, use

   julia> Pkg.build()

2. Use the following to run all tests.

      julia> include(scriptdir("runtests.jl")

   Check folder scripts to run tests from individual papers.

3. The codes for [Araujo2022] depend on the package NLPModelsAlgencan.jl, which is a wrapper for Julia of ALGENCAN that uses NLPModels (and JuMP). Follow the instructions of NLPModelsAlgencan.jl to install it with HSL linear system solver support for faster results.

References

[Behling2023c] Behling, R., Bello-Cruz, Y., Iusem, A., Liu, D., and Santos, L.-R. “A finitely convergent circumcenter method for the Convex Feasibility Problem”, 2023. arXiv:2308.09849

[Behling2023b] Behling, R., Bello-Cruz, Y., Iusem, A., Liu, D., and Santos, L.-R. “A successive centralized circumcenter reflection method for the convex feasibility problem”, 2023. doi: 10.1007/s10589-023-00516-w

[Behling2023a] R. Behling, J.-Y. Bello-Cruz, A. N. Iusem and L.-R. Santos, “On the centralization of the circumcentered-reflection method”, Matehmatical Programming, 2023. doi: 10.1007/s10107-023-01978-w. arXiv:2111.07022.

[Arefidamghani2023] R. Arefidamghani, R. Behling, J.-Y. Bello-Cruz, A. N. Iusem, and L.-R. Santos, “A circumcentered-reflection method for finding common fixed points of firmly nonexpansive operators”, Journal of Applied and Numerical Optimization (to appear), 2023, arXiv:2203.02410.

[Araujo2022] G. Araújo, R. Arefidamghani, R. Behling, J.-Y. Bello-Cruz, A. N. Iusem, and L.-R. Santos, “Circumcentering approximate reflections for solving the convex feasibility problem”, Fixed Point Theory and Algorithms for Sciences and Engineering, 1, 2023 doi: 10.1186/s13663-021-00711-6 arXiv:2105.00497

[Behling2021] R. Behling, J.-Y. Bello-Cruz, and L.-R. Santos, “On the Circumcentered-Reflection Method for the Convex Feasibility Problem”, Numer. Algorithms, 86, p. 1475-1494 2021, doi: 10.1007/s11075-020-00941-6, arXiv:2001.01773.

[Arefidamghani2021] R. Arefidamghani, R. Behling, J.-Y. Bello-Cruz, A. N. Iusem, and L.-R. Santos, “The circumcentered-reflection method achieves better rates than alternating projections”, Comp Optim App, 79(2), p. 507–530, 2021, doi: 10.1007/s10589-021-00275-6, arXiv:2007.14466.