All of the examples can be found in Jupyter notebook form here.

Paper examples

using Convex, ECOS

Summation.

println("Summation example")
x = Variable();
e = 0;
@time begin
  for i = 1:1000
    global e
    e += x;
  end
  p = minimize(e, x>=1);
end
@time solve!(p, () -> ECOS.Optimizer(verbose=0))

Summation example
  0.013567 seconds (4.64 k allocations: 11.763 MiB)
  1.349140 seconds (2.13 M allocations: 106.883 MiB, 6.00% gc time)

Indexing.

println("Indexing example")
x = Variable(1000, 1);
e = 0;
@time begin
  for i = 1:1000
    global e
    e += x[i];
  end
  p = minimize(e, x >= ones(1000, 1));
end
@time solve!(p, () -> ECOS.Optimizer(verbose=0))

Indexing example
  0.146036 seconds (126.00 k allocations: 17.675 MiB)
  0.117719 seconds (175.28 k allocations: 80.086 MiB, 35.29% gc time)

Matrix constraints.

println("Matrix constraint example")
n, m, p = 100, 100, 100
X = Variable(m, n);
A = randn(p, m);
b = randn(p, n);
@time begin
  p = minimize(norm(vec(X)), A * X == b);
end
@time solve!(p, () -> ECOS.Optimizer(verbose=0))

Matrix constraint example
  0.174976 seconds (262.83 k allocations: 12.309 MiB, 7.72% gc time)
  2.567839 seconds (865.58 k allocations: 379.401 MiB, 23.96% gc time)

Transpose.

println("Transpose example")
X = Variable(5, 5);
A = randn(5, 5);
@time begin
  p = minimize(norm2(X - A), X' == X);
end
@time solve!(p, () -> ECOS.Optimizer(verbose=0))

n = 3
A = randn(n, n);
#@time begin
  X = Variable(n, n);
  p = minimize(norm(vec(X' - A)), X[1,1] == 1);
  solve!(p, () -> ECOS.Optimizer(verbose=0))
#end

Transpose example
  0.052721 seconds (76.61 k allocations: 3.772 MiB, 19.07% gc time)
  0.029236 seconds (41.06 k allocations: 2.125 MiB)

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