You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: README.md
+33-11Lines changed: 33 additions & 11 deletions
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -41,19 +41,41 @@ Please refer to the documentation.
41
41
## References
42
42
43
43
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
44
-
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.
44
+
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
45
+
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
45
46
46
47
```bibtex
47
-
@article{aravkin-baraldi-orban-2022,
48
-
author = {Aravkin, Aleksandr Y. and Baraldi, Robert and Orban, Dominique},
49
-
title = {A Proximal Quasi-{N}ewton Trust-Region Method for Nonsmooth Regularized Optimization},
50
-
journal = {SIAM Journal on Optimization},
51
-
volume = {32},
52
-
number = {2},
53
-
pages = {900--929},
54
-
year = {2022},
55
-
doi = {10.1137/21M1409536},
56
-
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. }
48
+
@article{ aravkin-baraldi-orban-2022,
49
+
author = {Aravkin, Aleksandr Y. and Baraldi, Robert and Orban, Dominique},
50
+
title = {A Proximal Quasi-{N}ewton Trust-Region Method for Nonsmooth Regularized Optimization},
51
+
journal = {SIAM J. Optim.},
52
+
year = 2022,
53
+
volume = 32,
54
+
number = 2,
55
+
pages = {900--929},
56
+
doi = {10.1137/21M1409536},
57
+
}
58
+
59
+
@article{ aravkin-baraldi-orban-2024,
60
+
author = {A. Y. Aravkin and R. Baraldi and D. Orban},
61
+
title = {A {L}evenberg–{M}arquardt Method for Nonsmooth Regularized Least Squares},
62
+
journal = {SIAM J. Sci. Comput.},
63
+
year = 2024,
64
+
volume = 46,
65
+
number = 4,
66
+
pages = {A2557--A2581},
67
+
doi = {10.1137/22M1538971},
68
+
}
69
+
70
+
@article{ leconte-orban-2025,
71
+
author = {G. Leconte and D. Orban},
72
+
title = {The Indefinite Proximal Gradient Method},
0 commit comments