Accelerated Distributed Nesterov Optimization Subject to Complex Constraints and Its Applications

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 54; no. 4; pp. 2055 - 2066
• Main Authors: Liu, Bing, Du, Wenli, Li, Zhongmei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Complex constraints; Convergence; distributed optimization; Estimation; Heuristic algorithms; Linear programming; Nesterov gradient descent; Optimization; parameter projection; Parameter uncertainty; plant-wide ethylene optimization; Production; Signal processing algorithms; Stability analysis; Topology
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2023.3331334

This article proposes a distributed optimization approach upon an undirected topology, through only local computation and communication, with the goal of optimizing global function which consists of a host of local functions under complex constraints. In particular, the accelerated distributed Nesterov gradient descent subject to complex constraints (Acc-DNGD-CCs) algorithm is developed for smooth and strongly convex functions. By adopting an estimation mechanism of gradient and only using the history information, the fast optimization of the presented algorithm is ensured. Subsequently, the parameter projection scheme is employed for handling constraints of uncertain parameters introduced by the coupling relationship between the nodes. Meanwhile, the rigorous theoretical proofs along with stability analysis are given to prove the linear convergence of the Acc-DNGD-CC algorithm. Furthermore, compared with some existing algorithms, the superior performances of Acc-DNGD-CC are verified by numerical simulation on a plant-wide ethylene separation optimization process in terms of energy saving.