Proximal algorithms (also known as "splitting" algorithms or methods) for nonsmooth optimization in Julia.
This package can be used in combination with ProximalOperators.jl (providing first-order primitives, i.e. gradient and proximal mapping, for numerous cost functions) and AbstractOperators.jl (providing several linear and nonlinear operators) to formulate and solve a wide spectrum of nonsmooth optimization problems.
StructuredOptimization.jl provides a higher-level interface to formulate and solve problems using (some of) the algorithms here included.
To install the package, simply issue the following command in the Julia REPL:
] add ProximalAlgorithms
Check out these test scripts for examples on how to apply the provided algorithms to problems.
|Douglas-Rachford splitting algorithm||
|Forward-backward splitting (i.e. proximal gradient) algorithm||
|Vũ-Condat primal-dual algorithm||
||, , |
|Davis-Yin splitting algorithm||
|Asymmetric forward-backward-adjoint algorithm||
|Douglas-Rachford line-search (L-BFGS)||
Contributions are welcome in the form of issues notification or pull requests. We recommend looking at already implemented algorithms to get inspiration on how to structure new ones.
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 Themelis, Stella, Patrinos, Douglas-Rachford splitting and ADMM for nonconvex optimization: Accelerated and Newton-type algorithms, arXiv preprint (2020).