Push-Sum Based Algorithm for Constrained Convex Optimization Problem and Its Potential Application in Smart Grid

Dear Editor, This letter aims to investigate the optimization problem where the decision variable is contained in a closed convex set. By combing the gradient decent-like method with the push-sum algorithm framework, we design the distributed iterative formulas under the condition that the considered graphs sequence is time-varying and unbalanced. Under some standard assumptions on the problem setting and the decaying step-sizes, we analyze the convergence property of the generated variables sequence under the proposed iterative formulas.

Automated summary

This letter investigates the optimization problem using a combination of gradient descent method with push-sum algorithm framework to design distributed iterative formulas for time-varying and unbalanced graphs. The convergence property of the generated variable sequence under the proposed iterative formulas is analyzed.