R. Luo, R. Bourdais, T.J.J. van den Boom, and B. De Schutter, "Properties of applying a resource allocation coordination algorithm to optimization problems with discrete decision variables," Tech. rep. 15-025, Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands, Sept. 2015.
This addendum contains the proof of the optimality conditions and the proof of the oscillation detecting conditions for discrete decision variables when the resource allocation coordination algorithm is directly applied to optimization problems with discrete decision variables. Those conditions are used in the paper "Multi-agent model predictive control based on resource allocation coordination for a class of hybrid systems with limited information sharing" by R. Luo, R. Bourdais, T.J.J. van den Boom and B. De Schutter, Engineering Applications of Artificial Intelligence, vol. 58, pp. 123-133, 2017.