Given data with shape = (t,m,n)
, I need to find a vector variable of shape (n,)
that minimizes a convex function of the data and vector. I've used cvxopt (and cvxpy) to perform convex optimizations using 2D input, but it seems like they don't support 3D arrays. Is there a way to implement this convex optimization using these or other similar packages?
Given data with shape (t,m,n)
and (t,m)
and var with shape (n,)
, here's a simplification of the type of function I need to minimize:
import numpy as np
obj_func(var,data1,data2):
#data1.shape = (t,m,n)
#data2.shape = (t,m)
#var.shape = (n,)
score = np.sum(data1*var,axis=2) #dot product along axis 2
time_series = np.sum(score*data2,axis=1) #weighted sum along axis 1
return np.sum(time_series)-np.sum(time_series**2) #some function
This seems like it should be a simple convex optimization, but unfortunately these functions aren't supported on N-dimensional arrays in cvxopt/cvxpy. Is there a way to implement this?
I think if you simply reshape data1
to be 2d temporarily you'll be fine, e.g.
import numpy as np
import cvxpy as cp
t, m, n = 10, 8, 6
data1 = np.ones((t, m, n))
data2 = np.ones((t, m))
x = cp.Variable(n)
score = cp.reshape(data1.reshape(-1, n) * x, (t, m))
time_series = cp.sum(cp.multiply(score, data2), axis=1)
expr = cp.sum(time_series) - cp.sum(time_series ** 2)
print(repr(expr))
Outputs:
Expression(CONCAVE, UNKNOWN, ())