# Obtain gradient of function at end of iterations in Optim.jl

**URL:** <https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244>\
**Category:** Optimization (Mathematical)\
**Tags:** optim\
**Created:** [June 2, 2021, 2:55am UTC](https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244 "2021-06-02T02:55:50Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![amrods](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/amrods/32/2543_2.png) [@amrods](https://discourse.julialang.org/u/amrods)\
**Post date:** [June 2, 2021, 2:55am UTC](https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244/1 "2021-06-02T02:55:50Z")

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Is it possible to obtain the gradient of the objective function at the iterations limit? There is a field in the object returned that is named `g_residual`, that would give me the max norm of the gradient, but I am interested in obtaining the gradient vector. Is there a way to obtain that gradient?

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 2, 2021, 11:14pm UTC](https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244/2 "2021-06-02T23:14:54Z")

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Assuming you didn’t pass an analytic gradient, just use `ForwardDiff`:

```nohighlight
using ForwardDiff
ForwardDiff.gradient(f, x)

```

It’s what Optim uses internally.

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<div class="post-metadata">

**Author:** ![amrods](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/amrods/32/2543_2.png) [@amrods](https://discourse.julialang.org/u/amrods)\
**Post date:** [June 2, 2021, 11:50pm UTC](https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244/3 "2021-06-02T23:50:14Z")

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I was hoping to piggy back on the work done by Optim. The way you propose I would have to pay for precompilation. I guess if I had supplied the gradient, then I could that without penalty, maybe I should do that.

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 3, 2021, 12:02am UTC](https://discourse.julialang.org/t/obtain-gradient-of-function-at-end-of-iterations-in-optim-jl/62244/4 "2021-06-03T00:02:53Z")

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Is recompilation really an issue?

```nohighlight
julia> using Optim, ForwardDiff

julia> f(x) = (x[1] - 2)^2 + 3
f (generic function with 1 method)

julia> r = optimize(f, [1.0], BFGS())
 * Status: success

 * Candidate solution
    Final objective value: 3.000000e+00

 * Found with
    Algorithm: BFGS

 * Convergence measures
    |x - x'| = 1.00e+00 ≰ 0.0e+00
    |x - x'|/|x'| = 5.00e-01 ≰ 0.0e+00
    |f(x) - f(x')| = 1.00e+00 ≰ 0.0e+00
    |f(x) - f(x')|/|f(x')| = 3.33e-01 ≰ 0.0e+00
    |g(x)| = 1.83e-11 ≤ 1.0e-08

 * Work counters
    Seconds run: 1 (vs limit Inf)
    Iterations: 1
    f(x) calls: 3
    ∇f(x) calls: 3

julia> xstar = Optim.minimizer(r)
1-element Vector{Float64}:
 2.0000000000069598

julia> @time ForwardDiff.gradient(f, xstar)
  0.840569 seconds (2.92 M allocations: 176.158 MiB, 7.48% gc time, 99.96% compilation time)
1-element Vector{Float64}:
 1.3919532193540363e-11

```