GPDPS GPDPS is a Julia package that provides the reference implementation of the generalized primal-dual proximal splitting approach described in the paper "Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization" by Christian Clason, Stanislav Mazurenko, and Tuomo Valkonen. Usage To use the provided test codes (compatible with Julia version 1.0-1.2, tested on macOS and Linux x86_64): start Julia from this directory with julia --project=. (or with the relative path to the GPDPS.jl directory from somewhere else) do ]instantiate to download all dependencies (only required the first time, make sure you go back to standard Julia prompt with backspace afterwards) (highly recommended: using Revise so you can make changes in the code without having to restart Julia; if not install, start julia (without --project) and ]add Revise) load the package with using GPDPS To run the example for the elliptic Nash equilibrium problem: do test_enep(N), where N controls the discretization (number of nodes per coordinate, default N=128) To run the example for the Huber-Potts segmentation model: do test_potts(alpha,gamma,keyword=value), where keyword is one or more of the following (comma separated, order insensitive, may be removed before submission) with default value if omitted: image: test image; default is "blobs" (size 256x254), other images in .tif format can be specified by file name if placed in the img folder isotropic: use isotropic (value true, default) or anisotropic (value `false)` Potts model maxit: maximum number of iterations (default 500000) If alpha or gamma are not specified, the default values 1 and 1e-3 are used. Possible issues: on macOS, it may also be required to ]add QuartzImageIO if it is not included in the default environment. Development This code can also be found at https://github.com/clason/GPDPS.jl Reference If you find this code useful, you can cite the paper as @article{GPDPS, author = {Clason, Christian and Mazurenko, Stanislav and Valkonen, Tuomo}, title = {Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization}, year = {2019}, eprinttype = {arxiv}, eprint = {1901.02746}, }