# Converting quadratic constrains to linear constraint [closed]

I try to convert a quadratic constraint to a linear one: $$w_j = \sum w_\text{j,i} \\ w_\text{j,i} = \frac{w_j}{D} \times u \\ w_j,D,u \in \mathbb{N} \\$$ The values for $$w_j$$ and $$D$$ are constant and does not change.
In fact, I try to divide the value of $$w_j$$ to pieces, defined by $$D$$. For example: $$D = 4$$ and $$w_j = 100$$ with $$w_\text{j,0},w_\text{j,1} \in {0,25,50,100}$$.

At first: Is there a way to express such a case with linear constraints?
At second: Is there a rule how to convert quadratic to linear constraints?

• There does not appear to be anything quadratic in what you wrote. Can you please edit the question and clarify it a bit?
– prubin
Commented Jun 16, 2022 at 23:18
• As I understand the docs of gurobi, I though every multiplikation aka division leads to quadratic constraints. Are these constraints still linear?
– Mike
Commented Jun 17, 2022 at 8:02
• Is it linear, because $w_j$ and $D$ are constant values? And would it be quadratic if $w_j$ and $D$ would be a decesion variable?
– Mike
Commented Jun 17, 2022 at 8:26
• Yes it is linear in the decision variable $u$ which is the important thing. Had $w$ and $u$ been decision variables it would be bilinear (i.e. special case of quadratic) , and if $w$, $D$ and $u$ all had been decision variables it would still have been bilinear as you would write it as the bilinear equality $w_{j,i} D = w_j u$ Commented Jun 17, 2022 at 12:30