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@@ -63,8 +63,8 @@ The package offers a consistent API to formulate optimization problems and apply
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It integrates seamlessly with the [JuliaSmoothOptimizers](https://github.com/JuliaSmoothOptimizers) ecosystem, an academic organization for nonlinear optimization software development, testing, and benchmarking.
-**Definition of smooth problems $f$** via [NLPModels.jl](https://github.com/JuliaSmoothOptimizers/NLPModels.jl)@[orban-siqueira-nlpmodels-2020] which provides a standardized Julia API for representing nonlinear programming (NLP) problems.
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Large collections of such problems are available in [Cutest.jl](https://github.com/JuliaSmoothOptimizers/CUTEst.jl)@[orban-siqueira-cutest-2020] and [OptimizationProblems.jl](https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl).
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-**Definition of smooth problems $f$** via [NLPModels.jl](https://github.com/JuliaSmoothOptimizers/NLPModels.jl)[@orban-siqueira-nlpmodels-2020] which provides a standardized Julia API for representing nonlinear programming (NLP) problems.
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Large collections of such problems are available in [Cutest.jl](https://github.com/JuliaSmoothOptimizers/CUTEst.jl)[@orban-siqueira-cutest-2020] and [OptimizationProblems.jl](https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl)[@migot-orban-siqueira-optimizationproblems-2023].
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Another option is to use [RegularizedProblems.jl](https://github.com/JuliaSmoothOptimizers/RegularizedProblems.jl), which provides instances commonly used in the nonsmooth optimization literature.
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-**Hessian approximations (quasi-Newton, diagonal approximations)** via [LinearOperators.jl](https://github.com/JuliaSmoothOptimizers/LinearOperators.jl), which represents Hessians as linear operators and implements efficient Hessian–vector products.
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-**Definition of nonsmooth terms $h$** via [ProximalOperators.jl](https://github.com/JuliaSmoothOptimizers/ProximalOperators.jl), which offers a large collection of nonsmooth functions, and [ShiftedProximalOperators.jl](https://github.com/JuliaSmoothOptimizers/ShiftedProximalOperators.jl), which provides shifted proximal mappings for nonsmooth functions.
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# Examples
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A simple example is the solution of a regularized quadratic problem with an $\ell_1$ penalty, as described in @[aravkin-baraldi-orban-2022].
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A simple example is the solution of a regularized quadratic problem with an $\ell_1$ penalty, as described in [@aravkin-baraldi-orban-2022].
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Such problems are common in statistical learning and compressed sensing applications.The formulation is
Another example is the FitzHugh-Nagumo inverse problem with an $\ell_1$ penalty, as described in @[aravkin-baraldi-orban-2022] and @[aravkin-baraldi-orban-2024].
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Another example is the FitzHugh-Nagumo inverse problem with an $\ell_1$ penalty, as described in [@aravkin-baraldi-orban-2022] and [@aravkin-baraldi-orban-2024].
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