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The growing dependence of electric power systems on gas-fired generators to balance fluctuating and intermittent production by renewable energy sources has increased the variation and volume of flows withdrawn from natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these dynamic conditions requires optimization methods that account for substantial intraday transients and can rapidly compute solutions in reaction to generator re-dispatch. Here, we present a computationally efficient method for minimizing gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The optimization method uses a simplified representation of gas flow physics, provides a choice of discretization schemes in time and space, and exploits a two-stage approach to minimize energy costs and ensure smooth and physically meaningful solutions. The resulting large-scale NLPs are solved using an interior point method. The optimization scheme is validated by comparing the solutions with an integration of the dynamic equations using an adaptive timestepping differential equation solver, as well as a different, recently proposed optimal control scheme. The comparison shows that solutions to the discretized problem are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme produces at least an order of magnitude reduction in computation time relative to the state of the art and scales to large gas transmission networks with more than 6,000 kilometers of total pipeline. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0821. [ABSTRACT FROM AUTHOR]