added: hessian keyword argument in NonLinMPC
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franckgaga
changed the title
hessian argument in NonLinMPChessian keyword argument in NonLinMPC
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Benchmark Results (Julia v1)Time benchmarks
Memory benchmarks
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Hi @franckgaga,
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This was referenced Nov 4, 2025
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Many thanks for the suggestions @gdalle. I tried to differentiate actual autodiff to decompression using
I benchmarked my case study with theses two options and it essentially changes nothing on the results, compared to
Alright thanks, I'm following it. The |
This doesn't look too bad, it's all blue and you're spending most of your time in the actual differentiation (gradients and hessians).
Here's the better implementation, which can be a thousand times faster (although it doesn't seem to impact your profiling). That's similar to what I'd like to do in SMC but I'm still figuring out API design for only filling one triangle. using LinearAlgebra, SparseArrays, StableRNGs
function copyto_lowertriangle_naive!(T::SparseMatrixCSC, A::SparseMatrixCSC)
for j in axes(A, 2)
for i in axes(A, 1)
if i >= j
T[i, j] = A[i, j]
end
end
end
return
end
function copyto_lowertriangle!(T::SparseMatrixCSC, A::SparseMatrixCSC)
@assert size(T) == size(A)
kT = 0
rvA, rvT = rowvals(A), rowvals(T)
nzA, nzT = nonzeros(A), nonzeros(T)
for j in axes(A, 2)
for kA in nzrange(A, j)
i = rvA[kA]
if i >= j
kT += 1
@assert i == rvT[kT]
nzT[kT] = nzA[kA]
end
end
end
return T
endBenchmark and test: julia> n, p = 1_000, 0.005;
julia> A = sparse(Symmetric(sprand(n, n, p)));
julia> T = similar(sparse(LowerTriangular(A)));
julia> copyto_lowertriangle!(T, A)
julia> T == LowerTriangular(A)
true
julia> using Chairmarks
julia> @b (T, A) copyto_lowertriangle_naive!(_[1], _[2])
7.881 ms
julia> @b (T, A) copyto_lowertriangle!(_[1], _[2])
12.958 μs |
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The new keyword argument allows enabling and customizing the computation of the Hessian of the Langrangian function. Note that this is only supported with
oracle=trueoption. Changing the Hessian backend will throw an error iforacle=false.The default is
hessian=false, meaning Hessian is not computed, and the Quasi-newton approximation provided by the optimizer will be used (e.g. L-BFGS forIpopt.jl). The other options are:hessian=true: it will select an appropriate AD backend for the Hessian, which is:hessian=backend: usebackend::Abstractfor the computation of the Hessian.Also, pretty-printing
NonLinMPCwill now show thehessianbackend.