# Differences between NLsolve and Optim in solving system of equations

**URL:** <https://discourse.julialang.org/t/differences-between-nlsolve-and-optim-in-solving-system-of-equations/60467>\
**Category:** Optimization (Mathematical)\
**Created:** [May 3, 2021, 3:17pm UTC](https://discourse.julialang.org/t/differences-between-nlsolve-and-optim-in-solving-system-of-equations/60467 "2021-05-03T15:17:40Z")\
**Posts on this page:** 1\
**Showing post:** 14

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**Author:** ![longemen3000](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/longemen3000/32/7298_2.png) [@longemen3000](https://discourse.julialang.org/u/longemen3000)\
**Post date:** [May 5, 2021, 4:23am UTC](https://discourse.julialang.org/t/differences-between-nlsolve-and-optim-in-solving-system-of-equations/60467/14 "2021-05-05T04:23:00Z")

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I use NLSolvers for this. i had this function defined,as NLSolvers provides the bare minimum:

```julia
using NLSolvers,ForwardDiff
function nlsolve(f!,x0,method=TrustRegion(Newton(), Dogleg()),options=NEqOptions())
    len = length(x0)
    xcache = zeros(eltype(x0),len)
    Fcache = zeros(eltype(x0),len)
    JCache = zeros(eltype(x0),len,len)
    jconfig = ForwardDiff.JacobianConfig(f!,x0,x0)
    function j!(J,x)
        #@show J
        ForwardDiff.jacobian!(J,f!,Fcache,x,jconfig)
    end
    function fj!(F,J,x) 
        #@show J,F
        ForwardDiff.jacobian!(J,f!,F,x,jconfig)
        F,J
    end
    
    function jv!(x)
        function JacV(Fv,v)
            ForwardDiff.jacobian!(JCache,f!,Fcache,v,jconfig)
            Fv .= Jcache * v
        end
        return LinearMap(JacV,length(x))
    end
    vectorobj = NLSolvers.VectorObjective(f!,j!,fj!,jv!)
    vectorprob = NEqProblem(vectorobj)
    res = solve(vectorprob, x0,method , options)
end

```

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