Primal-Dual Algorithm for Distributed Optimization with Coupled Constraints

• Published in: Journal of optimization theory and applications Vol. 201; no. 1; pp. 252 - 279
• Main Authors: Gong, Kai, Zhang, Liwei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2024; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Approximation; Calculus of Variations and Optimal Control; Optimization; Constraints; Convergence; Decomposition; Engineering; Machine learning; Mathematics; Mathematics and Statistics; Methods; Multiagent systems; Operations Research/Decision Theory; Optimization; Theory of Computation; Variables; Distributed optimization; Time-varying networks; Coupled constraints; Convergence
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-024-02393-7

This paper focuses on distributed consensus optimization problems with coupled constraints over time-varying multi-agent networks, where the global objective is the finite sum of all agents’ private local objective functions, and decision variables of agents are subject to coupled equality and inequality constraints and a compact convex subset. Each agent exchanges information with its neighbors and processes local data. They cooperate to agree on a consensual decision vector that is an optimal solution to the considered optimization problems. We integrate ideas behind dynamic average consensus and primal-dual methods to develop a distributed algorithm and establish its sublinear convergence rate. In numerical simulations, to illustrate the effectiveness of the proposed algorithm, we compare it with some related methods by the Neyman–Pearson classification problem.