`NLSolvers.converged(ci::ConvergenceInfo)`

[longemen3000]

i'm rewiewing some code that uses optim, and it uses the x_converged, g_converged and f_converged fields of OptimizationResults. at the moment, there are some functions with the same name, but not defined on the ConvergenceInfo object. a mockup (based on show(io,mime,ci::ConvergenceInfo) would be the following:

x_converged(ci::NLSolvers.ConvergenceInfo) = false
f_converged(ci::NLSolvers.ConvergenceInfo) = false
g_converged(ci::NLSolvers.ConvergenceInfo) = false

function x_converged(ci::NLSolvers.ConvergenceInfo{<:NLSolvers.NelderMead,<:Any,<:NLSolvers.OptimizationOptions})
    return ci.info.ρs <= ci.options.x_abstol
end

function x_converged(ci::NLSolvers.ConvergenceInfo{<:NLSolvers.SimulatedAnnealing,<:Any,<:NLSolvers.OptimizationOptions})
    #don't know what to do do here, simulated annealing does not "converge" in the typical sense
    return true
end

function x_converged(ci::NLSolvers.ConvergenceInfo{<:Any,<:Any,<:NLSolvers.OptimizationOptions})
    info = ci.info
    opt = ci.options
    x_abstol = haskey(info, :ρs) && (info.ρ <= opt.x_abstol)
    x_reltol = haskey(info, :ρs) && (info.ρs/info.ρx <= opt.x_reltol)
    return x_abstol || x_reltol
end

function f_converged(ci::NLSolvers.ConvergenceInfo{<:Any,<:Any,<:NLSolvers.OptimizationOptions})
    info = ci.info
    opt = ci.options
    f_limit = !isfinite(opt.f_limit) || (info.minimum <= opt.f_limit)
    f_abstol = haskey(info, :fx) && (abs(info.fx - info.minimum) <= opt.f_abstol)
    f_reltol = haskey(info, :fx) && (abs((info.fx - info.minimum)/info.fx) <= opt.f_reltol)
    return f_limit || f_abstol || f_reltol
end

function f_converged(ci::NLSolvers.ConvergenceInfo{<:Any,<:Any,<:NLSolvers.NEqOptions})
    ρF = norm(ci.info.best_residual, Inf)
    #ρFz = norm(ci.info.solution, 2)
    f_abstol = ρF <= opt.f_abstol
    return f_abstol
end

function g_converged(ci::NLSolvers.ConvergenceInfo{<:Any,<:Any,<:NLSolvers.OptimizationOptions})
    info = ci.info
    opt = ci.options
    if haskey(info, :∇fz)
        ρ∇f = opt.g_norm(info.∇fz)
        g_abstol = ρP<=opt.g_abstol
        g_reltol = ρ∇f/info.∇f0<=opt.g_reltol
        if haskey(info, :prob) && hasbounds(info.prob)
            ρP = opt.g_norm(
                info.solution .- clamp.(info.solution .- info.∇fz, info.prob.bounds...),
            )
            gp_abstol = ρP <= opt.g_abstol
        else
            gp_abstol = false
        end
    else
        g_abstol =  false
        g_reltol = false
    end
    return g_abstol || g_reltol || gp_abstol
end

function converged(ci::NLSolvers.ConvergenceInfo)
    opt = ci.options
    info = ci.info
    conv_flags = x_converged(ci) || f_converged(ci) || g_converged(ci)
    if haskey(info, :Δ)
        Δmin = ci.solver.Δupdate.Δmin isa Nothing ? 0 : ci.solver.Δupdate.Δmin
        Δ = info.Δ <= Δmin
        Δ_finite = isfinite(info.Δ)
    else
        Δ = false
        Δ_finite = true
    end
    x = x_converged(ci)
    f = f_converged(ci)
    g = g_converged(ci)
    #finite flags
    x_finite = all(isfinite,NLSolvers.solution(ci))
    conv_flags = f || x || g || Δ
    finite_flags = x_finite && Δ_finite #  && g_finite && f_finite
    return conv_flags && finite_flags
end

what is missing is a general way to calculate the finiteness of the other stopping criteria, to address https://github.com/JuliaNLSolvers/Optim.jl/pull/997