`TrustRegion` cannot solve the Readme example from NLsolve.jl

[junyuan-chen]

If I didn't misunderstand how the solver is supposed to be used, there must be issues with TrustRegion. Also, what seems strange to me is that there is no warning message or something like that when the residuals are far from zeros. Somehow the solver just terminates quietly.

function f!(F, x, p)
    F[1] = (x[1]+3)*(x[2]^3-7)+18
    F[2] = sin(x[2]*exp(x[1])-1)
end

function j!(J, x, p)
    J[1, 1] = x[2]^3-7
    J[1, 2] = 3*x[2]^2*(x[1]+3)
    u = exp(x[1])*cos(x[2]*exp(x[1])-1)
    J[2, 1] = x[2]*u
    J[2, 2] = u
end

x0 = [0.1, 1.2]
F = NonlinearFunction(f!, jac=j!)
prob = NonlinearProblem(F, x0)
solver = solve(prob, TrustRegion(), reltol=1e-8)

Running above gives:

julia> solver = solve(prob, TrustRegion(), reltol=1e-8)
u: 2-element Vector{Float64}:
 0.22839632925361786
 1.1261248602773282

julia> solver.resid
2-element Vector{Float64}:
 0.011709310458734024
 0.40325365258870505

[ChrisRackauckas]

This is a duplicate of #142.

Note that I just pulled them from the docs for this reason. bf6bcce