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test_socp.jl
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test_socp.jl
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using Convex
using FactCheck
TOL = 1e-3
facts("SOCP Atoms") do
context("norm 2 atom") do
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
p = minimize(norm2(A * x + b))
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(0.64888, TOL)
@fact evaluate(norm2(A * x + b)) => roughly(0.64888, TOL)
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
lambda = 1
p = minimize(norm2(A * x + b) + lambda * norm2(x), x >= 1)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(14.9049, TOL)
@fact evaluate(norm2(A * x + b) + lambda * norm2(x)) => roughly(14.9049, TOL)
x = Variable(2)
p = minimize(norm2([x[1] + 2x[2] + 2, 2x[1] + x[2] + 3, 3x[1]+4x[2] + 4]) + lambda * norm2(x), x >= 1)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(14.9049, TOL)
@fact evaluate(norm2(A * x + b) + lambda * norm2(x)) => roughly(14.9049, TOL)
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
lambda = 1
p = minimize(norm2(A * x + b) + lambda * norm_1(x), x >= 1)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(15.4907, TOL)
@fact evaluate(norm2(A * x + b) + lambda * norm_1(x)) => roughly(15.4907, TOL)
end
context("frobenius norm atom") do
m = Variable(4, 5)
c = [m[3, 3] == 4, m >= 1]
p = minimize(vecnorm(m, 2), c)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(sqrt(35), TOL)
@fact evaluate(vecnorm(m, 2)) => roughly(sqrt(35), TOL)
end
context("quad over lin atom") do
x = Variable(3, 1)
A = [2 -3 5; -2 9 -3; 5 -8 3]
b = [-3; 9; 5]
c = [3 2 4]
d = -3
p = minimize(quadoverlin(A*x + b, c*x + d))
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(17.7831, TOL)
@fact evaluate(quadoverlin(A*x + b, c*x + d))[1] => roughly(17.7831, TOL)
end
context("sum squares atom") do
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
p = minimize(sumsquares(A*x + b))
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(0.42105, TOL)
@fact evaluate(sumsquares(A*x + b))[1] => roughly(0.42105, TOL)
end
context("square atom") do
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
p = minimize(sum(square(A*x + b)))
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(0.42105, TOL)
@fact evaluate(sum(square(A*x + b))) => roughly(0.42105, TOL)
x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
b = [2; 3; 4]
expr = A * x + b
p = minimize(sum(expr * expr))
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(0.42105, TOL)
@fact evaluate(sum(expr * expr)) => roughly(0.42105, TOL)
end
context("inv pos atom") do
x = Variable(4)
p = minimize(sum(invpos(x)), invpos(x) < 2, x > 1, x == 2, 2 == x)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(2, TOL)
@fact evaluate(sum(invpos(x))) => roughly(2, TOL)
end
context("geo mean atom") do
x = Variable(2)
y = Variable(2)
p = minimize(geomean(x, y), x >= 1, y >= 2)
# not DCP compliant
@fact vexity(p) => ConcaveVexity()
p = maximize(geomean(x, y), 1 < x, x < 2, y < 2)
# Just gave it a vector as an objective, not okay
@fact_throws solve!(p)
p = maximize(sum(geomean(x, y)), 1 < x, x < 2, y < 2)
solve!(p)
@fact p.optval => roughly(4, TOL)
@fact evaluate(sum(geomean(x, y))) => roughly(4, TOL)
end
context("sqrt atom") do
x = Variable()
p = maximize(sqrt(x), 1 >= x)
end
context("quad form atom") do
x = Variable(3, 1)
A = [0.8608 0.3131 0.5458; 0.3131 0.8584 0.5836; 0.5458 0.5836 1.5422]
p = minimize(quadform(x, A), [x >= 1])
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(6.1464, TOL)
@fact evaluate(quadform(x, A))[1] => roughly(6.1464, TOL)
x = Variable(3, 1)
A = -1.0*[0.8608 0.3131 0.5458; 0.3131 0.8584 0.5836; 0.5458 0.5836 1.5422]
c = [3 2 4]
p = maximize(c*x , [quadform(x, A) >= -1])
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(3.7713, TOL)
@fact evaluate(quadform(x, A))[1] => roughly(-1, TOL)
end
context("huber atom") do
x = Variable(3)
p = minimize(sum(huber(x, 1)), x >= 2)
@fact vexity(p) => ConvexVexity()
solve!(p)
@fact p.optval => roughly(9, TOL)
@fact evaluate(sum(huber(x, 1))) => roughly(9, TOL)
end
context("rational norm atom") do
A = [1 2 3; -1 2 3];
b = A * ones(3);
x = Variable(3);
p = minimize(norm(x, 4.5), [A * x == b]);
@fact vexity(p) => ConvexVexity()
# Solution is approximately x = [1, .93138, 1.04575]
solve!(p)
@fact p.optval => roughly(1.2717, TOL)
@fact evaluate(norm(x, 4.5)) => roughly(1.2717, TOL)
end
context("rational norm dual norm") do
v = [0.463339, 0.0216084, -2.07914, 0.99581, 0.889391];
x = Variable(5);
q = 1.379; # q norm constraint that generates many inequalities
qs = q / (q - 1); # Conjugate to q
p = minimize(x' * v);
p.constraints += (norm(x, q) <= 1);
@fact vexity(p) => ConvexVexity()
solve!(p) # Solution is -norm(v, q / (q - 1))
@fact p.optval => roughly(-2.144087, TOL)
@fact sum(evaluate(x' * v)) => roughly(-2.144087, TOL)
@fact evaluate(norm(x, q)) => roughly(1, TOL)
@fact sum(evaluate(x' * v)) => roughly(-sum(abs(v).^qs)^(1/qs), TOL);
end
context("rational norm atom sum") do
A = [-0.719255 -0.229089;
-1.33632 -1.37121;
0.703447 -1.4482];
b = [-1.82041, -1.67516, -0.866884];
q = 1.5;
xvar = Variable(2);
p = minimize(.5 * sumsquares(xvar) + norm(A * xvar - b, q));
@fact vexity(p) => ConvexVexity();
solve!(p)
# Compute gradient, check it is zero(ish)
x_opt = xvar.value;
margins = A * x_opt - b;
qs = q / (q - 1); # Conjugate
denom = sum(abs(margins).^q)^(1/qs);
g = x_opt + A' * (abs(margins).^(q-1) .* sign(margins)) / denom;
@fact p.optval => roughly(1.7227, TOL);
@fact norm(g, 2)^2 => roughly(0, TOL);
end
context("norm consistent with Base") do
A = randn(4, 4)
x = Variable(4, 4)
x.value = A
@fact evaluate(norm(x)) => roughly(norm(A), TOL);
@fact evaluate(norm(x, 1)) => roughly(norm(A, 1), TOL);
@fact evaluate(norm(x, 2)) => roughly(norm(A, 2), TOL);
@fact evaluate(norm(x, Inf)) => roughly(norm(A, Inf), TOL);
@fact evaluate(vecnorm(x, 1)) => roughly(norm(vec(A), 1), TOL);
@fact evaluate(vecnorm(x, 2)) => roughly(norm(vec(A), 2), TOL);
@fact evaluate(vecnorm(x, 7)) => roughly(norm(vec(A), 7), TOL);
@fact evaluate(vecnorm(x, Inf)) => roughly(norm(vec(A), Inf), TOL);
end
end