A classification of methods for distributed system optimization based on formulation structure

This paper presents a classification of formulations for distributed system optimization based on formulation structure. Two main classes are identified: nested formulations and alternating formulations. Nested formulations are bilevel programming problems where optimization subproblems are nested in the functions of a coordinating master problem. Alternating formulations iterate between solving a master problem and disciplinary subproblems in a sequential scheme. Methods included in the former class are collaborative optimization and BLISS2000. The latter class includes concurrent subspace optimization, analytical target cascading, and augmented Lagrangian coordination. Although the distinction between nested and alternating formulations has not been made in earlier comparisons, it plays a crucial role in the theoretical and computational properties of distributed optimization methods. The most prominent general characteristics for each class are discussed in more detail, providing valuable insights for the theoretical analysis and further development of distributed optimization methods.