快速稳定的非凸约束分布式优化问题：ELLADA算法
Fast and Stable Nonconvex Constrained Distributed Optimization: The ELLADA Algorithm
摘要：
分布式优化是一种解决大规模优化问题的有前途的方法，其中使用多个代理以局部和协调的方式执行计算，例如，在大规模工厂的模型预测控制（MPC）中出现的那些。然而，分布式优化算法，计算效率高，全局收敛，服从非凸约束和一般的子系统间的相互作用仍然是一个悬而未决的问题。在本文中，我们结合了三个重要的修改，经典的交替方向的乘法器（ADMM）的分布式优化。具体而言，（i）一个额外的层结构，以适应非凸性和处理不等式约束，（ii）等式约束的非线性规划（NLP）问题被允许近似解决，（iii）一个修改的安德森加速，以减少迭代次数。理论收敛到固定的解决方案和计算复杂性的算法，命名为ELLADA，建立。它的应用程序的分布式非线性预测控制也描述和说明通过一个基准过程系统。
英文摘要：
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.
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