setintersectionprojection.jl's Introduction

SetIntersectionProjection

Julia software for computing:

projections onto intersections of convex and non-convex constraint sets Documentation
projections onto a generalization of the Minkowski set. Documentation

This software is based on the papers:

@article{peters2019algorithms,
  title={Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems},
  author={Peters, Bas and Herrmann, Felix J},
  journal={arXiv preprint arXiv:1902.09699},
  year={2019}
}

and

@article{peters2019generalized,
  title={Generalized Minkowski sets for the regularization of inverse problems},
  author={Peters, Bas and Herrmann, Felix J},
  journal={arXiv preprint arXiv:1903.03942},
  year={2019}
}

Installation for Julia 1.6:

add SetIntersectionProjection

The examples also use the packages:
- MAT
- PyPlot
- StatsBase
- InvertibleNetworks
- TestImages
- Images
- Flux

Status:

January 2022

improved the l1-ball projection code, in terms of reduced computation times.
master branch works with Julia 1.5 & 1.6
timings for each part of the PARSDMM algorithm are now available as log_PARSDMM.timing after solving a projection problem as (x1,log_PARSDMM) = PARSDMM(m,AtA,TD_OP,set_Prop,P_sub,comp_grid,options)
Recently added full support for custom JOLI operators, some examples can be found here.
see https://github.com/slimgroup/ConstrainedFWIExamples for some more examples of how to use this package as the projector in combination with other software packages that compute function values and gradients for PDE-constrained optimization.
The waveform inversion example illustrates how SetIntersectionProjection can work together with other packages in other Julia versions (requires some package installations in Julia 0.6)
the V06 branch works with Julia 0.6 and is intended only for the waveform inversion example that uses WAVEFORM.jl

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