Many network flows nowadays, especially in a data center environment, have associated deadlines by which they must be fully transmitted. Nevertheless, traditional transport protocols such as TCP, focus on concepts like throughput and fairness, and do not aim to satisfy flow deadlines. Motivated by this limitation, several alternative transport designs and solutions have been recently proposed. These approaches generally achieve a better performance in terms of the number of satisfied deadlines and are usually built upon various heuristics. In contrast to these previous works, this article approaches the problem directly from an optimization perspective. We first prove that the problem belongs to the class of NP-hard problems that do not even admit a constant ratio approximation solution (unless P=NP), and formulate it as a mixed integer-linear optimization program. Then, using linear programming approximations, we further develop offline and online optimization-based rate control algorithms to approach the problem. Flow-level simulation results indicate that the proposed algorithms can be near-optimal, and hence they can be served as benchmarks against which other solutions to this problem can be evaluated. We additionally performed simulations incorporating such real network features as deployment delays and packet-level granularity to evaluate the performance of the proposed algorithms in a more realistic environment.