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