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)||
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 Tseng, On Accelerated Proximal Gradient Methods for Convex-Concave Optimization (2008).
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 Vũ, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Advances in Computational Mathematics, vol. 38, no. 3, pp. 667-681 (2013).
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 Latafat, Patrinos, Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators, Computational Optimization and Applications, vol. 68, no. 1, pp. 57-93 (2017).
 Stella, Themelis, Sopasakis, Patrinos, A simple and efficient algorithm for nonlinear model predictive control, 56th IEEE Conference on Decision and Control (2017).
 Themelis, Stella, Patrinos, Forward-backward envelope for the sum of two nonconvex functions: Further properties and nonmonotone line-search algorithms, SIAM Journal on Optimization, vol. 28, no. 3, pp. 2274–2303 (2018).
 Themelis, Stella, Patrinos, Douglas-Rachford splitting and ADMM for nonconvex optimization: Accelerated and Newton-type algorithms, arXiv preprint (2020).
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