Distributed optimization in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
State Agreement for Continuous-Time Coupled Nonlinear Systems
SIAM Journal on Control and Optimization
Reaching a Consensus in a Dynamically Changing Environment: A Graphical Approach
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Incremental Stochastic Subgradient Algorithms for Convex Optimization
SIAM Journal on Optimization
A Randomized Incremental Subgradient Method for Distributed Optimization in Networked Systems
SIAM Journal on Optimization
Tracking control for multi-agent consensus with an active leader and variable topology
Automatica (Journal of IFAC)
IEEE Transactions on Information Theory
Randomized consensus algorithms over large scale networks
IEEE Journal on Selected Areas in Communications
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In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min"z"@?"R"^"d@?"i"="1^nf"i(z), in which the optimal solution set of objective function f"i can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step.