Distributed initialization-free algorithms for multi-agent optimization problems with coupled inequality constraints

Abstract This paper studies a resource optimization problem for a multi-agent network where all agents have local objective functions and local constraint sets. Meanwhile, the decision variables of all the agents need to satisfy a set of globally coupled inequality constraints. Then, a distributed continuous-time algorithm is designed with the help of the nonsmooth analysis theory and projection operator method. The proposed algorithm does not require each agent to send the gradient information of the cost function to its neighbors, which prevents the gradient information of agents leaking out. Moreover, the convergence analysis shows that the proposed algorithm can converge to the optimal solution starting from any initial allocation. Finally, a case study is presented for a resource allocation problem of a hybrid water-power network.

[1]  Yiguang Hong,et al.  Distributed Continuous-Time Algorithm for Constrained Convex Optimizations via Nonsmooth Analysis Approach , 2015, IEEE Transactions on Automatic Control.

[2]  Ashish Cherukuri,et al.  Distributed Generator Coordination for Initialization and Anytime Optimization in Economic Dispatch , 2015, IEEE Transactions on Control of Network Systems.

[3]  Qing-Long Han,et al.  Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach , 2019, IEEE Transactions on Cybernetics.

[4]  Zheng Yan,et al.  A Neurodynamic Approach to Distributed Optimization With Globally Coupled Constraints , 2018, IEEE Transactions on Cybernetics.

[5]  Sijie Chen,et al.  Distributed Neurodynamic Optimization for Energy Internet Management , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[6]  Jiangping Hu,et al.  An ADMM Based Distributed Finite-Time Algorithm for Economic Dispatch Problems , 2018, IEEE Access.

[7]  Chris Reade,et al.  Distributed construction of minimum Connected Dominating Set in wireless sensor network using two-hop information , 2017, Comput. Networks.

[8]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[9]  Angelia Nedic,et al.  Subgradient Methods for Saddle-Point Problems , 2009, J. Optimization Theory and Applications.

[10]  Xing-Bao Gao,et al.  A novel neural network for nonlinear convex programming , 2004, IEEE Trans. Neural Networks.

[11]  Feng Liu,et al.  Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems , 2015, Autom..

[12]  Feng Liu,et al.  Distributed gradient algorithm for constrained optimization with application to load sharing in power systems , 2015, Syst. Control. Lett..

[13]  Asuman E. Ozdaglar,et al.  Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods , 2008, SIAM J. Optim..

[14]  Kaibo Shi,et al.  Distributed inexact dual consensus ADMM for network resource allocation , 2019 .

[15]  A. Ruszczynski,et al.  Nonlinear Optimization , 2006 .

[16]  John Langford,et al.  Scaling up machine learning: parallel and distributed approaches , 2011, KDD '11 Tutorials.

[17]  Ion Necoara,et al.  On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems , 2014, Autom..

[18]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[19]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[20]  Shu Liang,et al.  Distributed Continuous-Time Algorithms for Resource Allocation Problems Over Weight-Balanced Digraphs , 2018, IEEE Transactions on Cybernetics.

[21]  Stephen P. Boyd,et al.  Simultaneous routing and resource allocation via dual decomposition , 2004, IEEE Transactions on Communications.

[22]  Qing Ling,et al.  An Online Convex Optimization Approach to Proactive Network Resource Allocation , 2017, IEEE Transactions on Signal Processing.

[23]  Fernando Paganini,et al.  Stability of primal-dual gradient dynamics and applications to network optimization , 2010, Autom..

[24]  Wei Wang,et al.  Distributed Extremum Seeking for Optimal Resource Allocation and Its Application to Economic Dispatch in Smart Grids , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Shu Liang,et al.  Distributed Nonsmooth Optimization With Coupled Inequality Constraints via Modified Lagrangian Function , 2016, IEEE Transactions on Automatic Control.

[26]  Jiangping Hu,et al.  Distributed Inexact Consensus-Based ADMM Method for Multi-Agent Unconstrained Optimization Problem , 2019, IEEE Access.

[27]  Ashish Cherukuri,et al.  Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment , 2014, Autom..

[28]  Qingshan Liu,et al.  A Multi-Agent System With a Proportional-Integral Protocol for Distributed Constrained Optimization , 2017, IEEE Transactions on Automatic Control.

[29]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[30]  Enrique Mallada,et al.  Asymptotic convergence of constrained primal-dual dynamics , 2015, Syst. Control. Lett..

[31]  Zhu Wang,et al.  Distributed optimization for multi-agent systems with constraints set and communication time-delay over a directed graph , 2018, Inf. Sci..