equality constraints in robust optimization Is it possible to write the robust form of equality constraints in linear programming models? Or it is possible only for inequality constraints?
 A: It only makes sense to talk about uncertain equalities if you have products between the uncertainty and the decision variables and thus have the possibility to zero out the uncertain terms suitably.
As an example, let $x$ be decision variable and $w$ the uncertainty, and study the equality $x_1 + x_2 = w ~\forall ~w\in\mathcal{W}$. This makes makes no sense since there is no way to assign a fixed value to $x$ which holds for any $w$. The equation  $x_1 +x_2 = x_3 w ~\forall ~w\in\mathcal{W}$ is reasonable though, since a solution is given by $x_3=0$ and any pair satisfying $x_1+x_2=0$
A typical mistake in robust modeling is to read assignment as equality. The first constraint was perhaps meant to be $x_2$ is assigned the value $-x_1+w$. In other words, the expression $x_2$ is not a decision variable, but an affine function of the decision variable $x_1$ and uncertainty $w$. This mistake is very common in modelling of uncertain discrete-time systems, and similar problems with some kind of causality or direction. 
Another point-of-view is perhaps that you want $x_1$ and $x_2$ to be functions of $w$ (policies) and not fixed decision variables. In the first case, you might thus have a linear policy $x_1 = c_0 + c_1 w$ and $x_2 = d_0+d_1w$, where $c$ and $d$ are decision variables satisfying $c_0+d_0=0$ and $c_1+d_1 = 1$.
