The high complexity and time-varying workload of emerging multimedia applications poses a major challenge for dynamic voltage scaling (DVS) algorithms. Although many DVS algorithms have been proposed for real-time applications, an efficient method for evaluating the optimality of such DVS algorithms for multimedia applications does not yet exist. In this paper, we propose the first offline linear programming (LP) method to determine the minimum energy consumption for processing multimedia tasks under stringent delay deadlines. On the basis of the obtained energy lower bound, we evaluate the optimality of various existing DVS algorithms. Furthermore, we extend the LP formulation in order to construct an online DVS algorithm for real-time multimedia processing based on robust sequential linear programming. Simulation results obtained by decoding a wide range of video sequences show that, on average, our online algorithm provides a scheduling solution that requires less than 0.3% more energy than the optimal lower bound with only 0.03% miss rate. In comparison, a very recent algorithm consumes approximately 4% more energy than the optimal lower bound at the same miss rate.