Privacy Preservation in Distributed Optimization via Dual Decomposition and ADMM

In this work, we explore distributed optimization problems, as they are often stated in energy and resource optimization. More precisely, we consider systems consisting of a number of subsystems that are solely connected through linear constraints on the optimized solutions. The focus is put on two approaches; namely dual decomposition and alternating direction method of multipliers (ADMM), and we are interested in the case where it is desired to keep information about subsystems secret. To this end, we propose a privacy preserving algorithm based on secure multiparty computation (SMPC) and secret sharing that ensures privacy of the subsystems while converging to the optimal solution. To gain efficiency in our method, we modify the traditional ADMM algorithm.