Distributed Alternating Direction Method of Multipliers for Linearly Constrained Optimization

Distributed optimization plays an important role in solving engineering problems. Contrary to centralized optimization, it seeks to find global optima in a distributed manner, where agents within a group share information only with their neighbors. Optimizing a cost function without constraints or with separable constraints has already been addressed, however, it appears to be difficult to find an optimal solution when both cross-Terms and linear constraints exist. To solve this problem, we propose a distributed optimization algorithm based on alternating direction method of multipliers and dual ascent method. A simulation compares the performance of our algorithm with centralized dual ascent algorithm. Results show that our algorithm requires more iterations when the number of agents gets large, however, its distributed nature still makes it appropriate in many applications.