This repository contains a prototype implementation of the algorithms from the following paper:

V. Charisopoulos, D. Davis. A superlinearly convergent subgradient method for sharp semismooth problems, 2022. URL: https://arxiv.org/abs/2201.04611.

The implementation is available as a Julia package called SuperPolyak.jl, which can be embedded in other Julia applications. The core algorithms can be found under src/SuperPolyak.jl. Under scripts/, we have included all the scripts necessary to reproduce the numerical experiments in the paper. We recommend running the code using Julia 1.6 or later.

Note: We have also released a Pytorch version at SuperPolyak.py.

To install the dependencies of the package, run the following from the root directory of this repository:

$ julia --project=. -e 'import Pkg; Pkg.instantiate()'

To use the SuperPolyak package in an interactive session, open the Julia prompt using

$ julia --project=.

and enter import SuperPolyak in the Julia prompt, as you would with any other Julia package.

To install locally, enter the following in a Julia session:

julia> ]    # Enter Pkg mode
(@v1.6) pkg> add https://github.com/COR-OPT/SuperPolyak.jl

The commands below assume that the root of this repository is the current directory.

First, install all the necessary dependencies using

julia --project=scripts -e 'import Pkg; Pkg.instantiate()'

All the experiments in the paper are contained in individual scripts. For example, to solve a phase retrieval instance with dimension d = 100 and m = 250 measurements, we run:

julia --project=scripts scripts/phase_retrieval.jl --d 100 --m 250

To view the help text, including a description of the available arguments, simply run:

julia --project=scripts scripts/phase_retrieval.jl --help

The subdirectory includes scripts for solving the following problems:

• Phase retrieval (using both the subgradient and the alternating projections method)
• Quadratic sensing
• Bilinear sensing
• Max-linear regression
• ReLU regression
• Compressed sensing (using the alternating projections method)
• LASSO regression (using the proximal gradient method)