Convergence and stability of distributed stochastic time-varying iterative processes

This paper is devoted to the study of convergence analysis of distributed stochastic time-varying iterative processes arising in the applications of pseudogradient optimisation algorithms. The main techniques the authors used are the concepts of stochastic difference inequalities and the vector Lyapunov function, which are ideally suited to reducing the dimensionality problem arising in testing convergence of distributed parallel schemes. By applying the M-matrix conditions to a test matrix having a dimension equal to the number of the processors in the scheme, suitable scaling factors are selected each individual processor, which produce a satisfactory convergence rate of the overall iterative process. The results provide new convergence tests for distributed time-varying iterative processes arising in decentralized extremal regulation, adaptation, and parameter estimation schemes