A simple mirror of Chris Sims's csolve and csminwel optimization functions, originally written in MATLAB, which are available here.

The interfaces to the optimize function and OptimizationResults type are based on the analogous objects in the widely-known Optim.jl package, although SimsOptim.jl does not import & re-export Optim.jl. Future versions of SimsOptim.jl might do so, however.

the method signatures of optimize are

optimize(
    f::Function,
    g::Function, [optional]
    x0::Vector,
    m::Csolve;
    kwargs...
)

for the multidimensional Csolve procedure, and

optimize(
    f::Function,
    g::Function, [optional]
    H0::Matrix, [optional]
    x0::Vector,
    m::Csminwel;
    <keyword arguments>
)

for the unidimensional Csminwel procedure. the keyword arguments are shared between the two, with default values

f_tol::Real = 1e-14
g_tol::Real = 1e-8
x_tol::Real = 1e-32
iterations::Int = 1000 (Csolve algorithm) or 100 (Csminwel algorithm)
δ::Real = 1e-6
α::Real = 1e-3
verbose::Bool = false

The FiniteDifferences.jl package's jacobian and grad functions are used to approximate g for the Csolve and Csminwel algorithms, respectively. To change the finite-difference method settings, use the set_fdm_settings! function.

the SimsOptim package is registered; simply call Pkg.add("SimsOptim") at the REPL

using the two-dimensional Rosenbrock function

function rosen(z::AbstractVector{T}) where {T}
    a, b = 1, 100
    c, d = a, 150

    x, y = z[1], z[2]

    r = zeros(T, 2)
    r[1] = (a - x^2) + b * (x^2 - y)^2
    r[2] = (c - x^2) + d * (x^2 - y)^2

    return r
end

as an example, we can find its minimum easily:

julia> using Pkg; Pkg.add("SimsOptim")
julia> results = optimize(rosen, [0.5, 4], Csolve())

the optimize function returns an OptimizationResults instance, whose REPL representation is

status using Csolve(): success

convergence
----------------
    x: false
    f: true
    g: false

objectives
----------------
    value    : 5.069629645745414e-15
    minimum  : [2.0278518582981656e-15, 3.0417777874472484e-15]
    minimizer: [1.0, 1.0000000045031676]

counts
----------------
    total iterations: 29
    f calls         : 30
    g calls         : 30

improvements
----------------
    initial_x: [0.5, 4.0]
    x_change : [-0.5, 2.9999999954968324]
    f_change : [1407.0, 2110.125]
    g_size   : 2.00000540380114

information
----------------
    flag   : 0
    message: success

each of the listed fields above can be accessed by a non-exported function of the same name. for example,

julia> SimsOptim.minimizer(results)
2-element Vector{Float64}:
 1.0
 1.0000000045031676