In [1]:
using Optim
Optim.UnconstrainedProblems.examples["Rosenbrock"]
# These codes turn f and g into one function ... 
function opt_combine(x, f, g!)
    g = Vector{Float64}(length(x))
    g!(x,g)
    return (f(x), g)
end
function opt_problem(p::Optim.UnconstrainedProblems.OptimizationProblem)
    return x -> opt_combine(x, p.f, p.g!)
end
# this just makes it easy to use
opt_problem(s::AbstractString) = opt_problem(
    Optim.UnconstrainedProblems.examples[s])

# Here's an example 
fg = opt_problem("Himmelblau")
f, g = fg([0.0,0.0]) # show the function and gradient
Out[1]:
(170.0,[-14.0,-22.0])
In [2]:
problems = keys(Optim.UnconstrainedProblems.examples)
Out[2]:
Base.KeyIterator for a Dict{String,Optim.UnconstrainedProblems.OptimizationProblem} with 9 entries. Keys:
  "Exponential"
  "Fletcher-Powell"
  "Rosenbrock"
  "Parabola"
  "Hosaki"
  "Large Polynomial"
  "Polynomial"
  "Powell"
  "Himmelblau"
In [4]:
using Iterators
using Plots
plotlyjs()
"""
Make a line search plot that shows what the function
looks like in a direction p, with regions for the
strong Wolfe conditions satisfied. 
"""
function line_search_plot(fg, x, p; amax=1.0, c2 = 0.90, c1 = 0.1, npts=1000, strong=false)
    agrid = linspace(0,amax,npts)
    fvals = map(a -> fg(x + a*p)[1], agrid) # generate function values
    plt = plot(agrid, fvals, label="f")
    
    g0 = vecdot(fg(x)[2],p)
    f0 = fg(x)[1]
    
    plot!([agrid[1], agrid[end]],[f0,f0+c1*g0*agrid[end]],label="c1")
        
    gvals = map(a -> abs(vecdot(fg(x+a*p)[2],p)), agrid)
    
    if strong
        validwolfe = a -> (abs(vecdot(fg(x+a*p)[2],p)) <= c2*abs(g0)) * 
                          (fg(x + a*p)[1] <= f0+c1*g0*a)
    else
        validwolfe = a -> (vecdot(fg(x+a*p)[2],p) >= c2*g0) * 
                          (fg(x + a*p)[1] <= f0+c1*g0*a)
    end
    
    
    regions = groupby(validwolfe, agrid)
    for r in regions
        r1 = r[1]
        @show r1, r[end]
        
        if validwolfe(r1)
            plot!([r[1],r[end]], [f0, f0],fill=(0,:green,0.5),line=(0),label="c2")
        end
    end
   
    return plt
end
fg = opt_problem("Rosenbrock")
x = [0.0,0.0]
p = [1.0,0.0]
line_search_plot(fg, x, p; strong=false)
WARNING: Method definition line_search_plot(Any, Any, Any) in module Main at In[3]:10 overwritten at In[4]:10.
WARNING: Method definition #line_search_plot(Array{Any, 1}, Main.#line_search_plot, Any, Any, Any) in module Main overwritten.
WARNING: replacing docs for 'line_search_plot :: Tuple{Any,Any,Any}' in module 'Main'.
(r1,r[end]) = (0.0,0.05805805805805806)
(r1,r[end]) = (0.05905905905905906,0.24924924924924924)
(r1,r[end]) = (0.2502502502502503,1.0)
Out[4]:
In [5]:
fg = opt_problem("Himmelblau")
x = [0.0,0.0]
p = [1.0,0.0]
line_search_plot(fg, x, p; strong=false, amax=6)
(r1,r[end]) = (0.0,3.255255255255255)
(r1,r[end]) = (3.2612612612612613,4.852852852852853)
(r1,r[end]) = (4.858858858858859,6.0)
Out[5]:
In [10]:
fg = opt_problem("Himmelblau")
x = [0.0,0.0]
p = [1.0,0.0]
line_search_plot(fg, x, p; strong=true, amax=6, c1=1.0e-4, c2=0.99)
(r1,r[end]) = (0.0,3.2372372372372373)
(r1,r[end]) = (3.2432432432432434,3.5315315315315314)
(r1,r[end]) = (3.5375375375375375,6.0)
Out[10]:
In [7]:
using Plots
plotlyjs()
ezcontour(x, y, f) = begin
    X = repmat(x', length(y), 1)
    Y = repmat(y, 1, length(x))
    # Evaluate each f(x, y)
    Z = map((x,y) -> log(f([x,y])), X, Y)
    plot(x, y, Z, st=:contour)
end

function line_search_contour(fg, x, y, xk, p; amax=1.0)
    ezcontour(x, y, z -> fg(z)[1])
    scatter!([xk[1]],[xk[2]],label="")
    plot!([xk[1], xk[1] + amax*p[1]], [xk[2], xk[2] + amax*p[2]], label="")
end

line_search_contour(fg, -6:0.05:6, -6:0.05:6, x, p; amax=6.0)
Out[7]: