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lostella committed Jan 20, 2018
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[![Coverage Status](https://coveralls.io/repos/kul-forbes/ProximalAlgorithms.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/kul-forbes/ProximalAlgorithms.jl?branch=master)
[![codecov.io](http://codecov.io/github/kul-forbes/ProximalAlgorithms.jl/coverage.svg?branch=master)](http://codecov.io/github/kul-forbes/ProximalAlgorithms.jl?branch=master)

Proximal algorithms (also known as "splitting" algorithms) for nonsmooth optimization in Julia.
Proximal algorithms (also known as "splitting" algorithms or methods) for nonsmooth optimization in Julia.
This package can be used in combination with [ProximalOperators.jl](https://github.com/kul-forbes/ProximalOperators.jl) (providing first-order primitives, i.e. gradient and proximal mapping, for numerous cost functions) and [AbstractOperators.jl](https://github.com/kul-forbes/AbstractOperators.jl) (providing several linear and nonlinear operators) to formulate and solve a wide spectrum of nonsmooth optimization problems.

### Implemented Algorithms

Algorithm | Function | Reference
--------------------------------------|---------------|-----------
Asymmetric forward-backward-adjoint | `AFBA` ([AsymmetricForwardBackwardAdjoint.jl](src/algorithms/AsymmetricForwardBackwardAdjoint.jl)) | [[10]][latafat_2017]
Chambolle-Pock primal dual algorithm | `ChambollePock` ([AsymmetricForwardBackwardAdjoint.jl](src/algorithms/AsymmetricForwardBackwardAdjoint.jl)) | [[4]][chambolle_2011]
Douglas-Rachford splitting | `DRS` ([DouglasRachford.jl](src/algorithms/DouglasRachford.jl)) | [[1]][eckstein_1989]
(Fast) Forward-backward splitting | `FBS` ([ForwardBackward.jl](src/algorithms/ForwardBackward.jl)) | [[2]][tseng_2008], [[3]][beck_2009]
Vũ-Condat primal-dual algorithm | `VuCondat` ([AsymmetricForwardBackwardAdjoint.jl](src/algorithms/AsymmetricForwardBackwardAdjoint.jl)) | [[6]][vu_2013], [[7]][condat_2013]
ZeroFPR (L-BFGS) | `ZeroFPR` ([ZeroFPR.jl](src/algorithms/ZeroFPR.jl)) | [[9]][themelis_2016]
Asymmetric forward-backward-adjoint algorithm | [`AFBA`](src/algorithms/AsymmetricForwardBackwardAdjoint.jl) | [[10]][latafat_2017]
Chambolle-Pock primal dual algorithm | [`ChambollePock`](src/algorithms/AsymmetricForwardBackwardAdjoint.jl) | [[4]][chambolle_2011]
Douglas-Rachford splitting algorithm | [`DRS`](src/algorithms/DouglasRachford.jl) | [[1]][eckstein_1989]
Forward-backward splitting (i.e. proximal gradient) algorithm | [`FBS`](src/algorithms/ForwardBackward.jl) | [[2]][tseng_2008], [[3]][beck_2009]
Vũ-Condat primal-dual algorithm | [`VuCondat`](src/algorithms/AsymmetricForwardBackwardAdjoint.jl) | [[6]][vu_2013], [[7]][condat_2013]
ZeroFPR (L-BFGS) | [`ZeroFPR`](src/algorithms/ZeroFPR.jl) | [[9]][themelis_2016]

### References

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