A Distributed Algorithm for Optimal Energy Management With Network-Independent Stepsize

We propose a novel distributed algorithm, Dual-Primal Distributed Algorithm (DPDA), designed to achieve optimal energy management for supply-demand balance in a smart grid. For DPDA, a fixed and network-independent stepsize
$\beta > 0$
is used, which is sufficient to guarantee its convergence. Distinct from existing algorithms, each smart device does not need to access and exchange gradient information at each round of iteration. Furthermore, with general convexity, an
$o(1/k)$
convergence rate of DPDA is established, which is faster than
$O(1/k)$
rate.