I am trying to linearize the complementarity condition $0<a \perp b>0$ with SOS1 method by the following formulation:
$p_1+p_2 = 1e5 \label{1}\tag{1}$
$a < p_1\label{2}\tag{2}$
$b < p_2\label{3}\tag{3}$
where, $p_1$ and $p_2$ are the SOS1 variables. If equation \eqref{1} is set to 1, the problem becomes integer infeasible. If i set it to 1e5, both the variables attain values greater than 1. However, the definition of SOS1 says, at the most only 1 variable can take non zero value. Any clarification in this regard will be helpful.