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https://github.com/juliasmoothoptimizers/regularizedproblems.jl
Test Cases for Regularized Optimization
https://github.com/juliasmoothoptimizers/regularizedproblems.jl
julia optimization proximal-algorithms proximal-gradient-method proximal-operators proximal-regularization test-problems
Last synced: 9 days ago
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Test Cases for Regularized Optimization
- Host: GitHub
- URL: https://github.com/juliasmoothoptimizers/regularizedproblems.jl
- Owner: JuliaSmoothOptimizers
- License: other
- Created: 2021-08-03T02:17:46.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-04-23T18:55:46.000Z (8 months ago)
- Last Synced: 2024-04-24T13:09:19.210Z (8 months ago)
- Topics: julia, optimization, proximal-algorithms, proximal-gradient-method, proximal-operators, proximal-regularization, test-problems
- Language: Julia
- Homepage:
- Size: 510 KB
- Stars: 5
- Watchers: 3
- Forks: 5
- Open Issues: 7
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
- Citation: CITATION.bib
Awesome Lists containing this project
README
# RegularizedProblems.jl
[](https://github.com/JuliaSmoothOptimizers/RegularizedProblems.jl/actions/workflows/ci.yml)
[](https://JuliaSmoothOptimizers.github.io/RegularizedProblems.jl/dev)
[](https://codecov.io/gh/JuliaSmoothOptimizers/RegularizedProblems.jl)
[](https://zenodo.org/badge/latestdoi/392158884)
## How to cite
If you use RegularizedProblems.jl in your work, please cite using the format given in [CITATION.bib](CITATION.bib).
## Synopsis
`RegularizedProblems` is a repository of optimization problems implemented in pure Julia.
Contrary to what the name suggests, the problems are *not* regularized but they *should be*.
However, the choice of regularizer is left to the user.
The problems concerned by the package have the form
minimize f(x) + h(x)
where f: ℝⁿ → ℝ has Lipschitz-continuous gradient and h: ℝⁿ → ℝ is lower semi-continuous and proper.
The smooth term f describes the objective to minimize while the role of the regularizer h is to select
a solution with desirable properties: minimum norm, sparsity below a certain level, maximum sparsity, etc.
This repository gives access to several f terms.
Regularizers h should be taken from [ProximalOperators.jl](https://github.com/JuliaFirstOrder/ProximalOperators.jl).
## How to Install
Until this package is registered, use
```julia
pkg> add https://github.com/optimizers/RegularizedProblems.jl
```
## What is Implemented?
Please refer to the documentation.
## Related Software
* [ShiftedProximalOperators.jl](https://github.com/rjbaraldi/ShiftedProximalOperators)
* [RegularizedOptimization.jl](https://github.com/UW-AMO/RegularizedOptimization.jl)
## References
* 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
```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. }
}
```