Decentralized decomposition algorithms for peer-to-peer linear optimization

Abstract

We propose Decentralized Benders Decomposition and Decentralized Dantzig–Wolfe Decomposition algorithms for large-scale block angular linear programming problems. Our methods allow multiple peer decision makers to cooperate with the aim of solving the problem without the need of a central coordination mechanism. Instead we achieve cooperation by partial information sharing across a strongly connected communication network. Our main goal is to design decentralized solution approaches for decision makers who are unwilling to disclose their local data, but want to solve the global problem collaboratively for mutual benefit. We prove that our proposed methods reach global optimality in a finite number of iterations. We confirm our theoretical results with computational experiments.