``````

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]:

window.PLOTLYENV=window.PLOTLYENV || {};
window.PLOTLYENV.BASE_URL="https://plot.ly";
require(['plotly'], function(Plotly) {
Plotly.newPlot('9ac52915-cfad-41f7-9a05-d4aa5c22cada', 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{"yaxis":{"type":"-","titlefont":{"size":15,"color":"rgba(0, 0, 0, 1.000)","family":"sans-serif"},"title":"","tickfont":{"size":11,"color":"rgba(0, 0, 0, 1.000)","family":"sans-serif"},"ticks":"inside","tickmode":"array","showgrid":true,"tickvals":[0.0,20.0,40.0,60.0,80.0,100.0],"domain":[0.03762029746281716,0.9901574803149606],"ticktext":["0","20","40","60","80","100"],"tickangle":0,"zeroline":false,"linecolor":"rgba(0, 0, 0, 1.000)","tickcolor":"rgba(0, 0, 0, 1.000)","anchor":"x"},"annotations":[],"width":600,"plot_bgcolor":"rgba(255, 255, 255, 1.000)","showlegend":true,"legend":{"bgcolor":"rgba(255, 255, 255, 1.000)","y":1.0,"font":{"size":11,"color":"rgba(0, 0, 0, 1.000)","family":"sans-serif"},"bordercolor":"rgba(0, 0, 0, 1.000)","x":1.0},"xaxis":{"type":"-","titlefont":{"size":15,"color":"rgba(0, 0, 0, 1.000)","family":"sans-serif"},"title":"","tickfont":{"size":11,"color":"rgba(0, 0, 0, 1.000)","family":"sans-serif"},"ticks":"inside","tickmode":"array","showgrid":true,"tickvals":[0.0,0.2,0.4,0.6000000000000001,0.8,1.0],"domain":[0.05100612423447069,0.9934383202099737],"ticktext":["0.0","0.2","0.4","0.6","0.8","1.0"],"tickangle":0,"zeroline":false,"linecolor":"rgba(0, 0, 0, 1.000)","tickcolor":"rgba(0, 0, 0, 1.000)","anchor":"y"},"paper_bgcolor":"rgba(255, 255, 255, 1.000)","margin":{"r":0,"l":0,"b":0,"t":20},"height":400}, {showLink: false});

});

``````
``````

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]:

window.PLOTLYENV=window.PLOTLYENV || {};
window.PLOTLYENV.BASE_URL="https://plot.ly";
require(['plotly'], function(Plotly) {
Plotly.newPlot('30235d84-ddb3-4236-a49e-a11935e73e29', 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111, 71, 1.000)","shape":"linear"},"x":[0.0,6.0],"mode":"lines"},{"yaxis":"y","showlegend":true,"type":"scatter","xaxis":"x","name":"c2","fillcolor":"rgba(0, 128, 0, 0.500)","y":[170.0,170.0],"line":{"width":0,"dash":"solid","color":"rgba(62, 164, 78, 1.000)","shape":"linear"},"fill":"tozeroy","mode":"lines","x":[3.2612612612612613,4.852852852852853]}],
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});

``````
``````

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]:

window.PLOTLYENV=window.PLOTLYENV || {};
window.PLOTLYENV.BASE_URL="https://plot.ly";
require(['plotly'], function(Plotly) {
Plotly.newPlot('20048ae9-6a17-4e93-9bba-eec98a1dc779', 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});

``````
``````

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]:

window.PLOTLYENV=window.PLOTLYENV || {};
window.PLOTLYENV.BASE_URL="https://plot.ly";
require(['plotly'], function(Plotly) {
Plotly.newPlot('6bfd6bc0-bfb7-4c7a-8820-3655cbf91d57', 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