Distributed continuous-time algorithm for nonsmooth optimal consensus without sharing local decision variables

Abstract A distributed continuous-time algorithm is proposed for constrained nonsmooth convex optimization. A distinct feature of our algorithm is that it does not require agents to share their local decision variables to the network, and it still achieves the optimal solution. With the help of Lagrangian functions, exact penalty techniques, differential inclusions with maximal monotone maps and saddle-point dynamics, we prove the convergence of the proposed algorithm and show that it achieves an O(1/t) convergence rate. Numerical example also illustrates the effectiveness of the proposed method.

[1]  Qingshan Liu,et al.  A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization , 2015, IEEE Transactions on Automatic Control.

[2]  Ian R. Manchester,et al.  Dynamical Privacy in Distributed Computing -- Part II: PPSC Gossip Algorithms , 2018 .

[3]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

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

[5]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[6]  Tingwen Huang,et al.  A distributed continuous time consensus algorithm for maximize social welfare in micro grid , 2016, J. Frankl. Inst..

[7]  Ufuk Topcu,et al.  Differentially Private Distributed Constrained Optimization , 2014, IEEE Transactions on Automatic Control.

[8]  Pascal Bianchi,et al.  Robust Distributed Consensus Using Total Variation , 2016, IEEE Transactions on Automatic Control.

[9]  Shouyang Wang,et al.  Distributed continuous-time approximate projection protocols for shortest distance optimization problems , 2015, Autom..

[10]  Jorge Cortés,et al.  Differentially Private Distributed Convex Optimization via Functional Perturbation , 2015, IEEE Transactions on Control of Network Systems.

[11]  Bahman Gharesifard,et al.  Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs , 2012, IEEE Transactions on Automatic Control.

[12]  Gang Wang,et al.  Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs , 2017, J. Frankl. Inst..

[13]  Fuad E. Alsaadi,et al.  Recent advances on filtering and control for cyber-physical systems under security and resource constraints , 2016, J. Frankl. Inst..

[14]  Sabina Jeschke,et al.  Security and Privacy in Cyber-Physical Systems : Foundations, Principles, and Applications , 2017 .

[15]  Yang Lu,et al.  Privacy preserving distributed optimization using homomorphic encryption , 2018, Autom..

[16]  Karl Henrik Johansson,et al.  Reaching an Optimal Consensus: Dynamical Systems That Compute Intersections of Convex Sets , 2011, IEEE Transactions on Automatic Control.

[17]  Hyungbo Shim,et al.  Initialization-free Privacy-guaranteed Distributed Algorithm for Economic Dispatch Problem , 2018, Autom..

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

[19]  Lean Yu,et al.  Privacy Preservation in Distributed Subgradient Optimization Algorithms , 2015, IEEE Transactions on Cybernetics.

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