Buildings consume more than one-third of the world’s primary energy. Reducing energy use in buildings with energy efficient technologies is feasible and also driven by energy policies such as energy benchmarking, disclosure, rating, and labeling in both the developed and developing countries....

Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any p≥1 we define a stochastic algorithm which converges almost surely to the p-mean ep of μ. Assuming furthermore that the functional to minimize is regular around ep, we prove that a natural...