Problem does not follow DCP rules, while it does?

[siyuanpurdue]

I have an expression of this form: x[i] * cp.abs((lot+tau*all1)@v0). It is of type Expression(UNKNOWN, UNKNOWN, (2, 6)), which is surprising to me since I have follows.

x = cp.Variable(numNodes+1)

obj_constraints = []

I have constraints saying x are all non-negative.

for i in range(numNodes+1):
obj_constraints += [x[i] >= 0]

However, cp.abs((lot+tau * all1 ) @ v0) is Expression(CONVEX, NONNEGATIVE, (2, 6)).

x[i] is Expression(AFFINE, UNKNOWN, ())?? I thought x[i] should be non-negative so that the overall expression x[i] * cp.abs((lot+tau*all1)@v0) would be judged convex?

If I want to follow DCP rules, what should I do/formulate my expression/problem?

[siyuanpurdue]

Below is the complete error message:

DCPError: Problem does not follow DCP rules. Specifically:
The following constraints are not DCP:
reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2539[0, 0:12], (6, 1), F) == [[1. 0.]] @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F))) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]) + [[0.1 0.1]] @ abs([[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T , because the following subexpressions are not:
|-- reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2539[0, 0:12], (6, 1), F) == [[1. 0.]] @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F))) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]) + [[0.1 0.1]] @ abs([[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T
reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2540[0, 0:12], (6, 1), F) == Promote(var2538[0], (2, 6)) @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F)) + [[0.1 0.1]
[0.1 0.1]]) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T , because the following subexpressions are not:
|-- Promote(var2538[0], (2, 6)) @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F)) + [[0.1 0.1]
[0.1 0.1]]) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]])
reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2539[1, 0:12], (6, 1), F) == [[0. 1.]] @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F))) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]) + [[0.1 0.1]] @ abs([[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T , because the following subexpressions are not:
|-- reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2539[1, 0:12], (6, 1), F) == [[0. 1.]] @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F))) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]) + [[0.1 0.1]] @ abs([[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T
reshape([[ 1. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 1.]
[-1. 0. 0. 0. 0. 0.]
[ 0. -1. 0. 0. 0. 0.]
[ 0. 0. -1. 0. 0. 0.]
[ 0. 0. 0. -1. 0. 0.]
[ 0. 0. 0. 0. -1. 0.]
[ 0. 0. 0. 0. 0. -1.]].T @ var2540[1, 0:12], (6, 1), F) == Promote(var2538[1], (2, 6)) @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F)) + [[0.1 0.1]
[0.1 0.1]]) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]]).T , because the following subexpressions are not:
|-- Promote(var2538[1], (2, 6)) @ abs(([[1. 0.]
[0. 1.]] + -[[0.00015 0.00015]
[0.00015 0.0003 ]] @ diag_vec(reshape([[1. 0. 0.]
[0. 1. 0.]] @ var2538, (2,), F)) + [[0.1 0.1]
[0.1 0.1]]) @ [[ 0.00015 0.00015 -0.00015 -0.00015 -0.00015 -0.00015]
[ 0.00015 0.0003 -0.00015 -0.0003 -0.00015 -0.0003 ]])

[Transurgeon]

Hi @siyuanpurdue you can specify non-negativity constraints directly when you initialise your variables.

x = cp.Variable(numNodes+1, nonneg=True)

This should fix your issue :).

[siyuanpurdue]

Yes, I tried this and it did not work... @Transurgeon