A Stochastic Gradient-Based Projection Algorithm for Distributed Constrained Optimization

This paper investigates a category of constrained convex optimization problems, where the collective objective function is represented as the sum of all local objective functions subjected to local bounds and equality constraints. This kind of problems is important and can be formulated form a variety of applications, such as power control, sensor networks and source localization. To solve this problem more reliable and effective, we propose a novel distributed stochastic gradient-based projection algorithm under the presence of noisy gradients, where the gradients are infiltrated by arbitrary but uniformly bounded noise sample through local gradient observation. The proposed algorithm allows the adoption of constant step-size, which guarantees it can possess faster convergence rate compared with existing distributed algorithms with diminishing step-size. The effectiveness of the proposed algorithm is verified and testified by simulation experiments.