S-DIGing: A Stochastic Gradient Tracking Algorithm for Distributed Optimization

In this article, we study convex optimization problems where agents of a network cooperatively minimize the global objective function which consists multiple local functions. The intention work is to solve large-scale complicated, and numerous. Different from most existing works, each agent presented as average finite instantaneous Integrating gradient tracking algorithm with stochastic averaging technology, distributed (termed S-DIGing) proposed. At time instant, only one randomly selected an computed, applied approximate batch for agent. Based on novel primal-dual interpretation S-DIGing algorithm, it shown that linearly converges optimal solution when step-size do not exceed explicit upper bound, functions are strongly Lipschitz continuous gradients. Numerical experiments demonstrate practicability correctness theoretical results.