# Underdetermined system unsolvable

I am trying to solve Ax=b for an underdetermined system with an objective function based on weighted basis vectors.

I can’t seem to get a simple implementation to work, however. I have a very basic setup of my issues below.

First, the simple 3x3 square system works correctly:

``````# Objective is to satisfy Ax=b
# while minimizing weights * coefficients.
A = numpy.array([[0,0,1],[0,1,0],[1,0,0]])
x = cvx.Variable(len(A))
b = [1,2,3]

# weights
c = numpy.array([1, 1, 1])

obj = cvx.Minimize(c@x)
constraints = [A.T@x == b]
prob = cvx.Problem(obj, constraints)
result = prob.solve(solver="SCS")
print(x.value.round(), result.round())
``````
``````[3. 2. 1.] 6.0
``````

When I add another basis vector, however, the solver does not find a solution (even though there is one - `[2,1,0,1], 3.1`)

``````A = numpy.array([[0,0,1],[0,1,0],[1,0,0],[1,1,1]])
x = cvx.Variable(len(A))
b = [1,2,3]

c = numpy.array([1, 1, 1, 0.1])

obj = cvx.Minimize(c@x)
constraints = [A.T@x == b]
prob = cvx.Problem(obj, constraints)
result = prob.solve(solver="SCS")
print(x.value, result)
``````
``````None -inf
``````

So I wonder if I have defined my system wrong. Thanks so much for the help!!

This is the CVX forum. CVXPY is a different tool and has support at discord and elsewhere.

I’m not sure I am interpreting the output correctly, but it appears to be saying the problem is unbounded. So there is no “optimal” solution, even though there is a feasible solution (actually, an infinite number of them).

Apologies and I appreciate the reply