Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

[RFC] New Optimization API #17

Merged
merged 5 commits into from Apr 19, 2013
Merged

[RFC] New Optimization API #17

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
5 commits
Select commit Hold shift + click to select a range
1087b8d
First half of new optimization API
johnmyleswhite Mar 24, 2013
e769f72
More work on new optimization API
johnmyleswhite Mar 25, 2013
de40acf
New API design finished
johnmyleswhite Apr 18, 2013
ca3ee61
Fix missing keyword arguments
johnmyleswhite Apr 18, 2013
4709365
Fix state traces
johnmyleswhite Apr 18, 2013
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
239 changes: 136 additions & 103 deletions benchmarks/test_functions.jl
View file
Open in desktop
Expand Up @@ -5,23 +5,24 @@
##########################################################################

function fletcher_powell(x::Vector)
function theta(x::Vector)
if x[1] > 0
atan(x[2] / x[1]) / (2.0 * pi)
else
(pi + atan(x[2] / x[1])) / (2.0 * pi)
function theta(x::Vector)
if x[1] > 0
return atan(x[2] / x[1]) / (2.0 * pi)
else
return (pi + atan(x[2] / x[1])) / (2.0 * pi)
end
end
end

100.0 * (x[3] - 10.0 * theta(x[1], x[2]))^2 + (sqrt(x[1]^2 + x[2]^2) - 1.0)^2 + x[3]^2

return 100.0 * (x[3] - 10.0 * theta(x[1], x[2]))^2 +
(sqrt(x[1]^2 + x[2]^2) - 1.0)^2 + x[3]^2
end

function fletcher_powell_gradient(x::Vector)
error("Not yet defined")
function fletcher_powell_gradient(x::Vector, storage::Vector)
error("Not yet defined")
end

function fletcher_powell_hessian(x::Vector)
error("Not yet defined")
function fletcher_powell_hessian(x::Vector, storage::Matrix)
error("Not yet defined")
end

##########################################################################
Expand All @@ -31,15 +32,18 @@ end
##########################################################################

function himmelbrau(x::Vector)
(x[1]^2 + x[2] - 11)^2 + (x[1] + x[2]^2 - 7)^2
return (x[1]^2 + x[2] - 11)^2 + (x[1] + x[2]^2 - 7)^2
end

function himmelbrau_gradient(x::Vector)
[4.0 * x[1]^3 + 4.0 * x[1] * x[2] + 44.0 * x[1] + 2.0 * x[1] + 2.0 * x[2]^2 - 14.0,
2.0 * x[1]^2 + 2.0 * x[2] - 22.0 + 4.0 * x[1] * x[2] + 4.0 * x[2]^3 - 28.0 * x[2]]
function himmelbrau_gradient!(x::Vector, storage::Vector)
storage[1] = 4.0 * x[1]^3 + 4.0 * x[1] * x[2] +
44.0 * x[1] + 2.0 * x[1] + 2.0 * x[2]^2 - 14.0
storage[2] = 2.0 * x[1]^2 + 2.0 * x[2] - 22.0 +
4.0 * x[1] * x[2] + 4.0 * x[2]^3 - 28.0 * x[2]
end

function himmelbrau_hessian(x::Vector)
function himmelbrau_hessian!(x::Vector, storage::Matrix)
error("Not yet defined")
end

##########################################################################
Expand All @@ -49,23 +53,28 @@ end
##########################################################################

function parabola(x::Vector)
(1.0 - x[1])^2 +
(2.0 - x[2])^2 +
(3.0 - x[3])^2 +
(5.0 - x[4])^2 +
(8.0 - x[5])^2
end

function parabola_gradient(x::Vector)
[-2.0 * (1.0 - x[1]),
-2.0 * (2.0 - x[2]),
-2.0 * (3.0 - x[3]),
-2.0 * (5.0 - x[4]),
-2.0 * (8.0 - x[5])]
end

function parabola_hessian(x::Vector)
2.0 * eye(5)
return (1.0 - x[1])^2 + (2.0 - x[2])^2 + (3.0 - x[3])^2 +
(5.0 - x[4])^2 + (8.0 - x[5])^2
end

function parabola_gradient!(x::Vector, storage::Vector)
storage[1] = -2.0 * (1.0 - x[1])
storage[2] = -2.0 * (2.0 - x[2])
storage[3] = -2.0 * (3.0 - x[3])
storage[4] = -2.0 * (5.0 - x[4])
storage[5] = -2.0 * (8.0 - x[5])
end

function parabola_hessian!(x::Vector, storage::Matrix)
for i in 1:5
for j in 1:5
if i == j
storage[i, j] = 2.0
else
storage[i, j] = 0.0
end
end
end
end

##########################################################################
Expand All @@ -75,38 +84,34 @@ end
##########################################################################

function powell(x::Vector)
(x[1] + 10.0 * x[2])^2 +
5.0 * (x[3] - x[4])^2 +
(x[2] - 2.0 * x[3])^4 +
10.0 * (x[1] - x[4])^4
end

function powell_gradient(x::Vector)
[2.0 * (x[1] + 10.0 * x[2]) + 40.0 * (x[1] - x[4])^3,
20.0 * (x[1] + 10.0 * x[2]) + 4.0 * (x[2] - 2.0 * x[3])^3,
10.0 * (x[3] - x[4]) - 8.0 * (x[2] - 2.0 * x[3])^3,
-10.0 * (x[3] - x[4]) - 40.0 * (x[1] - x[4])^3]
end

function powell_hessian(x::Vector)
h = zeros(4, 4)
h[1, 1] = 2.0 + 120.0 * (x[1] - x[4])^2
h[1, 2] = 20.0
h[1, 3] = 0.0
h[1, 4] = 0.0
h[2, 1] = 20.0
h[2, 2] = 200.0 + 12.0 * (x[2] - 2.0 * x[3])^2
h[2, 3] = -24.0 * (x[2] - 2.0 * x[3])^2
h[2, 4] = 0.0
h[3, 1] = 0.0
h[3, 2] = -24.0 * (x[2] - 2.0 * x[3])^2
h[3, 3] = 10.0 + 48.0 * (x[2] - 2.0 * x[3])^2
h[3, 4] = -10.0
h[4, 1] = 0.0
h[4, 2] = 0.0
h[4, 3] = -10.0
h[4, 4] = 10.0 + 120.0 * (x[1] - x[4])^2
h
return (x[1] + 10.0 * x[2])^2 + 5.0 * (x[3] - x[4])^2 +
(x[2] - 2.0 * x[3])^4 + 10.0 * (x[1] - x[4])^4
end

function powell_gradient!(x::Vector, storage::Vector)
storage[1] = 2.0 * (x[1] + 10.0 * x[2]) + 40.0 * (x[1] - x[4])^3
storage[2] = 20.0 * (x[1] + 10.0 * x[2]) + 4.0 * (x[2] - 2.0 * x[3])^3
storage[3] = 10.0 * (x[3] - x[4]) - 8.0 * (x[2] - 2.0 * x[3])^3
storage[4] = -10.0 * (x[3] - x[4]) - 40.0 * (x[1] - x[4])^3
end

function powell_hessian!(x::Vector, storage::Matrix)
storage[1, 1] = 2.0 + 120.0 * (x[1] - x[4])^2
storage[1, 2] = 20.0
storage[1, 3] = 0.0
storage[1, 4] = 0.0
storage[2, 1] = 20.0
storage[2, 2] = 200.0 + 12.0 * (x[2] - 2.0 * x[3])^2
storage[2, 3] = -24.0 * (x[2] - 2.0 * x[3])^2
storage[2, 4] = 0.0
storage[3, 1] = 0.0
storage[3, 2] = -24.0 * (x[2] - 2.0 * x[3])^2
storage[3, 3] = 10.0 + 48.0 * (x[2] - 2.0 * x[3])^2
storage[3, 4] = -10.0
storage[4, 1] = 0.0
storage[4, 2] = 0.0
storage[4, 3] = -10.0
storage[4, 4] = 10.0 + 120.0 * (x[1] - x[4])^2
end

##########################################################################
Expand All @@ -116,21 +121,19 @@ end
##########################################################################

function rosenbrock(x::Vector)
(1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
return (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
end

function rosenbrock_gradient(x::Vector)
[-2.0 * (1.0 - x[1]) - 400.0 * (x[2] - x[1]^2) * x[1],
200.0 * (x[2] - x[1]^2)]
function rosenbrock_gradient!(x::Vector, storage::Vector)
storage[1] = -2.0 * (1.0 - x[1]) - 400.0 * (x[2] - x[1]^2) * x[1]
storage[2] = 200.0 * (x[2] - x[1]^2)
end

function rosenbrock_hessian(x::Vector)
h = zeros(2, 2)
h[1, 1] = 2.0 - 400.0 * x[2] + 1200.0 * x[1]^2
h[1, 2] = -400.0 * x[1]
h[2, 1] = -400.0 * x[1]
h[2, 2] = 200.0
h
function rosenbrock_hessian!(x::Vector, storage::Matrix)
storage[1, 1] = 2.0 - 400.0 * x[2] + 1200.0 * x[1]^2
storage[1, 2] = -400.0 * x[1]
storage[2, 1] = -400.0 * x[1]
storage[2, 2] = 200.0
end

##########################################################################
Expand All @@ -140,25 +143,25 @@ end
##########################################################################

function polynomial(x::Vector)
(10.0 - x[1])^2 + (7.0 - x[2])^4 + (108.0 - x[3])^4
return (10.0 - x[1])^2 + (7.0 - x[2])^4 + (108.0 - x[3])^4
end

function polynomial_gradient(x::Vector)
[-2.0 * (10.0 - x[1]), -4.0 * (7.0 - x[2])^3, -4.0 * (108.0 - x[3])^3]
function polynomial_gradient!(x::Vector, storage::Vector)
storage[1] = -2.0 * (10.0 - x[1])
storage[2] = -4.0 * (7.0 - x[2])^3
storage[3] = -4.0 * (108.0 - x[3])^3
end

function polynomial_hessian(x::Vector)
h = zeros(3, 3)
h[1, 1] = 2.0
h[1, 2] = 0.0
h[1, 3] = 0.0
h[2, 1] = 0.0
h[2, 2] = 12.0 * (7.0 - x[2])^2
h[2, 3] = 0.0
h[3, 1] = 0.0
h[3, 2] = 0.0
h[3, 3] = 12.0 * (108.0 - x[3])^2
h
function polynomial_hessian!(x::Vector, storage::Matrix)
storage[1, 1] = 2.0
storage[1, 2] = 0.0
storage[1, 3] = 0.0
storage[2, 1] = 0.0
storage[2, 2] = 12.0 * (7.0 - x[2])^2
storage[2, 3] = 0.0
storage[3, 1] = 0.0
storage[3, 2] = 0.0
storage[3, 3] = 12.0 * (108.0 - x[3])^2
end

##########################################################################
Expand All @@ -168,19 +171,49 @@ end
##########################################################################

function exponential(x::Vector)
exp((2.0 - x[1])^2) + exp((3.0 - x[2])^2)
return exp((2.0 - x[1])^2) + exp((3.0 - x[2])^2)
end

function exponential_gradient!(x::Vector, storage::Vector)
storage[1] = -2.0 * (2.0 - x[1]) * exp((2.0 - x[1])^2)
storage[2] = -2.0 * (3.0 - x[2]) * exp((3.0 - x[2])^2)
end

function exponential_hessian!(x::Vector, storage::Matrix)
storage[1, 1] = 2.0 * exp((2.0 - x[1])^2) * (2.0 * x[1]^2 - 8.0 * x[1] + 9)
storage[1, 2] = 0.0
storage[2, 1] = 0.0
storage[2, 2] = 2.0 * exp((3.0 - x[1])^2) * (2.0 * x[2]^2 - 12.0 * x[2] + 19)
end

function exponential_gradient(x::Vector)
[-2.0 * (2.0 - x[1]) * exp((2.0 - x[1])^2),
-2.0 * (3.0 - x[2]) * exp((3.0 - x[2])^2)]
##########################################################################
###
### Large-Scale Quadratic
###
##########################################################################

function large_polynomial(x::Vector)
res = 0.0
for i in 1:250
res += (i - x[i])^2
end
return res
end

function exponential_hessian(x::Vector)
h = zeros(2, 2)
h[1, 1] = 2.0 * exp((2.0 - x[1])^2) * (2.0 * x[1]^2 - 8.0 * x[1] + 9)
h[1, 2] = 0.0
h[2, 1] = 0.0
h[2, 2] = 2.0 * exp((3.0 - x[1])^2) * (2.0 * x[2]^2 - 12.0 * x[2] + 19)
h
function large_polynomial_gradient!(x::Vector, storage::Vector)
for i in 1:250
storage[i] = -2.0 * (i - x[i])
end
end

function large_polynomial_hessian!(x::Vector, storage::Matrix)
for i in 1:250
for j in 1:250
if i == j
storage[i, j] = 2.0
else
storage[i, j] = 0.0
end
end
end
end