results for R2

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 %\renewcommand{\year}{2020}     % If you don't want the current year.
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paper/report.bib

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+@Article{         aravkin-baraldi-orban-2022,
+  Author        = {Aravkin, A Y and Baraldi, R and Orban, D},
+  Title         = {A Proximal Quasi-{N}ewton Trust-Region Method for Nonsmooth Regularized Optimization},
+  Journal       = siopt,
+  Year          = 2022,
+  Volume        = 32,
+  Number        = 2,
+  Pages         = {900--929},
+  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-2024,
+  author = {Aravkin, Aleksandr Y. and Baraldi, Robert and Orban, Dominique},
+  title = {A {L}evenberg–{M}arquardt Method for Nonsmooth Regularized Least Squares},
+  journal = sisc,
+  volume = {46},
+  number = {4},
+  pages = {A2557--A2581},
+  year = {2024},
+  doi = {10.1137/22M1538971},
+  preprint = {https://www.gerad.ca/en/papers/G-2022-58/view},
+  abstract = { Abstract. We develop a Levenberg–Marquardt method for minimizing the sum of a smooth nonlinear least-squares term \(f(x) = \frac{1}{2} \|F(x)\|\_2^2\) and a nonsmooth term \(h\). Both \(f\) and \(h\) may be nonconvex. Steps are computed by minimizing the sum of a regularized linear least-squares model and a model of \(h\) using a first-order method such as the proximal gradient method. We establish global convergence to a first-order stationary point under the assumptions that \(F\) and its Jacobian are Lipschitz continuous and \(h\) is proper and lower semicontinuous. In the worst case, our method performs \(O(\epsilon^{-2})\) iterations to bring a measure of stationarity below \(\epsilon \in (0, 1)\). We also derive a trust-region variant that enjoys similar asymptotic worst-case iteration complexity as a special case of the trust-region algorithm of Aravkin, Baraldi, and Orban [SIAM J. Optim., 32 (2022), pp. 900–929]. We report numerical results on three examples: a group-lasso basis-pursuit denoise example, a nonlinear support vector machine, and parameter estimation in a neuroscience application. To implement those examples, we describe in detail how to evaluate proximal operators for separable \(h\) and for the group lasso with trust-region constraint. In all cases, the Levenberg–Marquardt methods perform fewer outer iterations than either a proximal gradient method with adaptive step length or a quasi-Newton trust-region method, neither of which exploit the least-squares structure of the problem. Our results also highlight the need for more sophisticated subproblem solvers than simple first-order methods. }
+}
+
+@TechReport{      aravkin-baraldi-leconte-orban-2021,
+  Author        = {Aravkin, Aleksandr Y. and Baraldi, Robert and Leconte, Geoffroy and Orban, Dominique},
+  Title         = {Corrigendum: A proximal quasi-{N}ewton trust-region method for nonsmooth regularized optimization},
+  Institution   = gerad,
+  Year          = 2024,
+  Type          = {Cahier},
+  Number        = {G-2021-12-SM},
+  Address       = gerad-address,
+  Pages         = {1--3},
+  doi           = {10.13140/RG.2.2.36250.45768},
+}
+
+@Book{            cartis-gould-toint-2022,
+  Author        = {Cartis, Coralia and Gould, Nicholas I. M. and Toint, {\relax Ph}ilippe L},
+  Title         = {Evaluation Complexity of algorithms for nonconvex optimization},
+  Publisher     = siam,
+  Year          = 2022,
+  Series        = {MOS-SIAM Series on Optimization},
+  Address       = siam-address,
+  doi           = {10.1137/1.9781611976991},
+  Number        = 30,
+}
+
+@techreport{diouane-habiboullah-orban-2024a,
+  author = {Y. Diouane and M. L. Habiboullah and D. Orban},
+  pages = {},
+  title = {Complexity of trust-region methods in the presence of unbounded Hessian approximations},
+  year = {2024},
+  number = {G-2024-43},
+  type = {Cahier},
+  institution = gerad,
+  address = gerad-address,
+  doi = {},
+  preprint = {https://www.gerad.ca/en/papers/G-2024-43},
+}
+
+@techreport{diouane-habiboullah-orban-2024b,
+  author = {Y. Diouane and M. L. Habiboullah and D. Orban},
+  pages = {},
+  title = {A Proximal Modified Quasi-{N}ewton Method for Nonsmooth Regularized Optimization},
+  year = {2024},
+  number = {G-2024-64},
+  type = {Cahier},
+  institution = gerad,
+  address = gerad-address,
+  doi = {10.13140/RG.2.2.21140.51840},
+  preprint = {https://www.gerad.ca/en/papers/G-2024-64},
+}
+
+@incollection{wright-2018,
+    author = {S. J. Wright},
+    title = {Optimization Algorithms for Data Analysis},
+    booktitle = {The Mathematics of Data},
+    publisher = ams,
+    editor = {M. W. Mahoney and J. C. Duchi and A. C. Gilbert},
+    volume = {25},
+    number = {},
+    series = {IAS/Park City Mathematics Series},
+    chapter = {2},
+    pages = {49--98},
+    address = ams-address,
+    edition = {1st},
+    year = {2018},
+    doi = {10.1090/pcms/025/00830},
+}