FirstOrderOptimizer.jl

module A

    using Optim
    import Optim: FirstOrderOptimizer, initial_state, update_state!, trace!, assess_convergence, AbstractOptimizerState, update!, value

    struct MinimalGradientDescent <: FirstOrderOptimizer
        η::Float64
    end

    MinimalGradientDescent(; η=1e-1) = MinimalGradientDescent(η)

    type MinimalGradientDescentState{T,N} <: AbstractOptimizerState
        x::Array{T,N}
        x_previous::Array{T,N}
        f_x_previous::T
    end

    function initial_state(method::MinimalGradientDescent, options, d, initial_x)
        # prepare cache variables etc here
        MinimalGradientDescentState(initial_x,initial_x,Inf)
    end

    function update_state!{T}(d, state::MinimalGradientDescentState{T}, method::MinimalGradientDescent)
        
        state.x += -method.η * gradient(d)
        
        false # should the procedure force quit?
    end
    
    function trace!(tr, d, state, iteration, method::MinimalGradientDescent, options)
            dt = Dict()
            if options.extended_trace
                dt["x"] = copy(state.x)
                dt["g(x)"] = copy(gradient(d))
            end
            g_norm = vecnorm(gradient(d), Inf)
            update!(tr,
            iteration,
            value(d),
            g_norm,
            dt,
            options.store_trace,
            options.show_trace,
            options.show_every,
            options.callback)
    end
    
    function assess_convergence(state::MinimalGradientDescentState, d, options)
        Optim.default_convergence_assessment(state, d, options)
    end
    
end


f = x -> sum(x.^2) + π
mfit = optimize(f,rand(2),A.MinimalGradientDescent(),Optim.Options(iterations=500,store_trace=true,extended_trace=true))