pythoncvxpy

How to sum part of a vector in `cvxpy`?

I am using cvxpy to solve a convex optimization problem, and here's my constraint:

enter image description here

So how can I express this constraint in cvxpy? The sum_entries function in cvxpy can only sum the whole matrix/vector, but not part of a vector.

Solution

  • Just select a subset by using indexing (in the following example: classic python-based slicing; but more complex indexing / numpy-style is possible):

    Example:

    from cvxpy import *

x = Variable(5)
constraints = []
constraints.append(x >= 0)   # all vars
constraints.append(x <= 10)  # all vars
constraints.append(sum_entries(x[:3]) <= 3)  # only part of vector; sum(first-three) <=3
objective = Maximize(sum_entries(x))
problem = Problem(objective, constraints)
problem.solve()
print(problem.status)
print(x.value.T)

    Output:

    optimal
[[  1.   1.   1.  10.  10.]]

    Note: as of cvxpy 1.0, sum_entries has been changed to sum

    I also suspect you are misunderstanding the problem here, but that formula-image is of course incomplete to be implemented.