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docs/src/guide/custom_objectives.jl

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#
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# Defining the proximal mapping for a custom function type requires adding a method for [`ProximalCore.prox!`](@ref).
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#
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# To compute gradients, algorithms use [`ProximalAlgorithms.value_and_gradient_closure`](@ref):
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# To compute gradients, algorithms use [`value_and_gradient_closure`](@ref):
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# this relies on [AbstractDifferentiation](https://github.com/JuliaDiff/AbstractDifferentiation.jl), for automatic differentiation
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# with any of its supported backends, when functions are wrapped in [`ProximalAlgorithms.AutoDifferentiable`](@ref),
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# with any of its supported backends, when functions are wrapped in [`AutoDifferentiable`](@ref),
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# as the examples below show.
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#
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# If however you would like to provide your own gradient implementation (e.g. for efficiency reasons),
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# you can simply implement a method for [`ProximalAlgorithms.value_and_gradient_closure`](@ref) on your own function type.
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# you can simply implement a method for [`value_and_gradient_closure`](@ref) on your own function type.
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#
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# ```@docs
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# ProximalCore.prox
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Counting(f::T) where {T} = Counting{T}(f, 0, 0, 0)
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# Now we only need to intercept any call to `value_and_gradient_closure` and `prox!` and increase counters there:
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# Now we only need to intercept any call to [`value_and_gradient_closure`](@ref) and [`prox!`](@ref) and increase counters there:
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function ProximalAlgorithms.value_and_gradient_closure(f::Counting, x)
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f.eval_count += 1

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