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Distributed optimization, where the computations are performed in a localized and coordinated manner using multiple agents, is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints and general inter-subsystem interactions remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers (ADMM) for distributed optimization. Specifically, (i) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (ii) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (iii) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence towards stationary solutions and computational complexity of the proposed algorithm, named ELLADA, is established. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system. 

Decomposition‐based solution algorithms for optimization problems depend on the underlying latent block structure of the problem. Methods for detecting this structure are currently lacking. In this article, we propose stochastic blockmodeling (SBM) as a systematic framework for learning the underlying block structure in generic optimization problems. SBM is a generative graph model in which nodes belong to some blocks and the interconnections among the nodes are stochastically dependent on their block affiliations. Hence, through parametric statistical inference, the interconnection patterns underlying optimization problems can be estimated. For benchmark optimization problems, we show that SBM can reveal the underlying block structure and that the estimated blocks can be used as the basis for decomposition‐based solution algorithms which can reach an optimum or bound estimates in reduced computational time. Finally, we present a general software platform for automated block structure detection and decomposition‐based solution following distributed and hierarchical optimization approaches.

 

Ease of control of complex networks has been assessed extensively in terms of structural controllability and observability, and minimum control energy criteria. Here we adopt a sparsity-promoting feedback control framework for undirected networks with Laplacian dynamics and distinct topological features. The control objective considered is to minimize the effect of disturbance signals, magnitude of control signals and cost of feedback channels. We show that depending on the cost of feedback channels, different complex network structures become the least expensive option to control. Specifically, increased cost of feedback channels favors organized topological complexity such as modularity and centralization. Thus, although sparse and heterogeneous undirected networks may require larger numbers of actuators and sensors for structural controllability, networks with Laplacian dynamics are shown to be easier to control when accounting for the cost of feedback channels.