Optimal energy-management by distributed, constrained gradient descent

This paper deals with distributed, constrained gradient descents in application to the optimization of an energy-management-problem. Two different solution strategies are considered. First, a decoupling approach is analyzed that employs a Lagrange approach to include the constraints in the objective function. By means of a counterexample it is shown that this procedure does not lead to the global optimum of the considered energy-management-problem in every case. The second strategy incorporates constraints by means of penalty-functions and solves the problem using the push-sum-consensus. The ensuing analysis by simulation is concerned with the difficulty of identifying the optimal parameter set and examines the convergence behavior with regard to different node and edge numbers of distinct communication graphs.