diff --git a/CITATION.bib b/CITATION.bib index f50c1897..5909c517 100644 --- a/CITATION.bib +++ b/CITATION.bib @@ -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-2026, + 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, + number = 118, + pages = 9344, + doi = {10.21105/joss.09344}, +} \ No newline at end of file diff --git a/README.md b/README.md index 3a2c82cf..2def282a 100644 --- a/README.md +++ b/README.md @@ -41,19 +41,41 @@ Please refer to the documentation. ## 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.A2557–A2581, 2024. Technical report: https://arxiv.org/abs/2301.02347 +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}, } ```