If you use ShiftedProximalOperators.jl in your work, please cite using the format given in CITATION.bib.
ShiftedProximalOperators is a library of proximal operators associated with proper lower-semicontinuous functions such as those implemented in ProximalOperators.jl for use in the algorithms implemented in RegularizedOptimization.jl.
The main difference between the proximal operators implemented in ProximalOperators.jl is that those implemented here involve a translation of the nonsmooth term. Specifically, this package considers proximal operators defined as
argmin { ½ ‖t - q‖₂² + ν h(x + s + t) + χ(s + t; ΔB) | t ∈ ℝⁿ },
where q is given, x and s are fixed shifts, h is the nonsmooth term with respect to which we are computing the proximal operator, and χ(.; ΔB) is the indicator of a ball of radius Δ defined by a certain norm.
Until this package is registered, use
pkg> add https://github.com/rjbaraldi/ShiftedProximalOperators.jlPlease refer to the documentation.
- A. Y. Aravkin, R. Baraldi and D. Orban, A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization, SIAM Journal on Optimization, 32(2), pp.900–929, 2022. Technical report: https://arxiv.org/abs/2103.15993