A parallel block scaled gradient method with decentralized step-size for block additive unconstrained optimization problems of large distributed systems

Abstract

In this paper, we propose a modified parallel block scaled gradient method for solving block additive unconstrained optimization problems of large distributed systems. Our method makes two major modifications to the typical parallel block scaled gradient method: First, we include a pre-processing step which reduces the computational time; second, we propose a decentralized Armijo-type step-size rule. This rule circumvents the difficulty of determining a step-size in a distributed computing environment and enables the proposed parallel algorithm to execute in a distributed computer network with a limited amount of data transfer. We have applied our method to the weighted-least-square problems of power system state estimation and demonstrated the convergence of our method by testing numerous examples on a PC network. The speedup ratio of the distributed version of our method tends to increase proportionally with the number of subsystems (or computers).