I have set of linear constraints and would like to find an answer to its unknown variables, $p_i$'s. One of my options to find a solution for $p_i$'s using maximum entropy problem, $\max(\sum - p_i \log p_i)$. However the condition $\sum p_i=1$ does not hold. I would like to know how necessary this condition is?
I have given this problem to a solver and it converges after a few iteration, however if I divide $p_i$ by a constant to satisfy the $\sum p_i=1$ the solver fails.