Abstract. Until now, the great majority of research in low-power systems has assumed a convex power model. However, recently, due to the confluence of emerging technological and architectural trends, standard convex models have been invalidated for the proper specification of power models with different execution speeds. For example, the use of a shutdown energy minimization strategy to eliminate leakage power in multiprocessor systems results in a non-convex trade-off between power and speed. Non-convexity renders the majority of previous power management schemes, algorithms, and even basic theorems invalid. For instance, the main premise that one has to run continuously using a single speed in order to minimize energy consumption for constant computation requirements is not valid anymore. We study techniques for energy minimization where the power versus speed curve has a non-convex shape. We first identify and quantify sources of non-convexity. Minimizing energy when the power-speed...