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These methods rely solely on the gradient and Hessian(-vector) information of the smooth part $f$ and the proximal mapping of the nonsmooth part $h$ in order to compute steps.
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Then, the objective function $f + h$ is used only to accept or reject trial points.
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Moreover, they can handle cases where Hessian approximations are unbounded[@diouane-habiboullah-orban-2024,@leconte-orban-2023-2], making the package particularly suited for large-scale, ill-conditioned, and nonsmooth problems.
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Moreover, they can handle cases where Hessian approximations are unbounded[@diouane-habiboullah-orban-2024] and [@leconte-orban-2023-2], making the package particularly suited for large-scale, ill-conditioned, and nonsmooth problems.
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# Statement of need
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@@ -77,7 +77,7 @@ The design of the package is motivated by recent advances in the complexity anal
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-**Model Hessians (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 $h$** via [ProximalOperators.jl](https://github.com/JuliaSmoothOptimizers/ProximalOperators.jl), which offers a large collection of nonsmooth terms $h$, and [ShiftedProximalOperators.jl](https://github.com/JuliaSmoothOptimizers/ShiftedProximalOperators.jl), which provides shifted proximal mappings.
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This modularity makes it easy to prototype, benchmark, and extend regularization-based methods [@diouane-habiboullah-orban-2024,@aravkin-baraldi-orban-2022,@aravkin-baraldi-orban-2024,@leconte-orban-2023-2,@diouane-gollier-orban-2024].
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This modularity makes it easy to prototype, benchmark, and extend regularization-based methods [@diouane-habiboullah-orban-2024],[@aravkin-baraldi-orban-2022],[@aravkin-baraldi-orban-2024],[@leconte-orban-2023-2] and [@diouane-gollier-orban-2024].
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