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18 changes: 10 additions & 8 deletions CITATION.bib
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@@ -1,8 +1,10 @@
@Misc{baraldi-diouane-gollier-habiboullah-leconte-orban-regularized-optimization-2024,
author = {R. Baraldi and Y. Diouane and M. Gollier and M. L. Habiboullah and G. Leconte and D. Orban},
title = {{RegularizedOptimization.jl}: Algorithms for Regularized Optimization},
month = {September},
howpublished = {\url{https://github.com/JuliaSmoothOptimizers/RegularizedOptimization.jl}},
year = {2024},
DOI = {10.5281/zenodo.6940313},
}
@Article{ gollier-habiboullah-leconte-baraldi-orban-diouane-2024,
Author = {M. Gollier and M. L. Habiboullah and G. Leconte and R. Baraldi and D. Orban and Y. Diouane},
Title = {{RegularizedOptimization.jl}: Algorithms for Regularized Optimization},
Journal = {Journal of Open Source Software},
Year = 2026,
Volume = 11,
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Number = 118,
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pages = 9344,
doi = {10.21105/joss.09344},
}
44 changes: 33 additions & 11 deletions README.md
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## References

1. 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
2. R. Baraldi, R. Kumar, and A. Aravkin (2019), [*Basis Pursuit De-noise with Non-smooth Constraints*](https://doi.org/10.1109/TSP.2019.2946029), IEEE Transactions on Signal Processing, vol. 67, no. 22, pp. 5811-5823.
2. A. Y. Aravkin, R. Baraldi and D. Orban, *A Levenberg-Marquardt Method for Nonsmooth Regularized Least Squares*, SIAM Journal on Scientific Computing, 46(4), pp.2557–2581, 2024. Technical report: https://arxiv.org/abs/2301.02347
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3. G. Leconte and D. Orban, *The Indefinite Proximal Gradient Method*, Computational Optimization and Applications, 91(2), pp.861–903, 2025. Technical report: https://arxiv.org/abs/2309.08433

```bibtex
@article{aravkin-baraldi-orban-2022,
author = {Aravkin, Aleksandr Y. and Baraldi, Robert and Orban, Dominique},
title = {A Proximal Quasi-{N}ewton Trust-Region Method for Nonsmooth Regularized Optimization},
journal = {SIAM Journal on Optimization},
volume = {32},
number = {2},
pages = {900--929},
year = {2022},
doi = {10.1137/21M1409536},
abstract = { We develop a trust-region method for minimizing the sum of a smooth term (f) and a nonsmooth term (h), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of (f + h) in a trust region. The model coincides with (f + h) in value and subdifferential at the center. We establish global convergence to a first-order stationary point when (f) satisfies a smoothness condition that holds, in particular, when it has a Lipschitz-continuous gradient, and (h) is proper and lower semicontinuous. The model of (h) is required to be proper, lower semi-continuous and prox-bounded. Under these weak assumptions, we establish a worst-case (O(1/\epsilon^2)) iteration complexity bound that matches the best known complexity bound of standard trust-region methods for smooth optimization. We detail a special instance, named TR-PG, in which we use a limited-memory quasi-Newton model of (f) and compute a step with the proximal gradient method, resulting in a practical proximal quasi-Newton method. We establish similar convergence properties and complexity bound for a quadratic regularization variant, named R2, and provide an interpretation as a proximal gradient method with adaptive step size for nonconvex problems. R2 may also be used to compute steps inside the trust-region method, resulting in an implementation named TR-R2. We describe our Julia implementations and report numerical results on inverse problems from sparse optimization and signal processing. Both TR-PG and TR-R2 exhibit promising performance and compare favorably with two linesearch proximal quasi-Newton methods based on convex models. }
@Article{ aravkin-baraldi-orban-2022,
Author = {Aravkin, Aleksandr Y. and Baraldi, Robert and Orban, Dominique},
Title = {A Proximal Quasi-{N}ewton Trust-Region Method for Nonsmooth Regularized Optimization},
Journal = {SIAM J. Optim.},
Year = 2022,
Volume = 32,
Number = 2,
Pages = {900--929},
doi = {10.1137/21M1409536},
}

@Article{ aravkin-baraldi-orban-2024,
Author = {A. Y. Aravkin and R. Baraldi and D. Orban},
Title = {A {L}evenberg–{M}arquardt Method for Nonsmooth Regularized Least Squares},
Journal = {SIAM J. Sci. Comput.},
Year = 2024,
Volume = 46,
Number = 4,
Pages = {A2557--A2581},
doi = {10.1137/22M1538971},
}

@Article{ leconte-orban-2025,
Author = {G. Leconte and D. Orban},
Title = {The Indefinite Proximal Gradient Method},
Journal = {Comput. Optim. Appl.},
Year = 2025,
Volume = 91,
Number = 2,
Pages = {861--903},
doi = {10.1007/s10589-024-00604-5},
}
```

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