I have studied different optimization techniques but found it challenging to come up with an efficient technique to solve my problem here. I am essentially looking for a computationally efficient (possibly a method with parallel execution) way to solve the following optimization problem (known as the entropy maximization):
$$min_N \sum_{ijt} N_{ij}^t log(N_{ij}^t) - N_{ij}^t $$
such that $$ \sum_{j} N_{ij}^t = O_{i}^{t} \quad \quad \forall it $$ $$ \sum_{it} N_{ij}^t = \sum_{t} O_{j}^{t} \quad \quad \forall j $$ $$ \sum_{ij} d_{ij} N_{ij}^t = V^t \sum_{i} O_{i}^{t} \quad \quad \forall t $$
The unknown here are the $N_{ij}^t$ for all $i,j,t$. We assume that the parameters $O$, $V$ and $d$ are well known.