A Convex Combination-Based Distributed Momentum Methods Over Directed Graphs

In this article, we introduce a convex combination-based distributed momentum method (CDM) for solving distributed optimization to minimize a sum of smooth and strongly convex local objective functions over directed graphs. The proposed method integrates the convex combination, row- and column-stochastic weights, and the adapt-then-combination rule. By selecting different parameters, it can be reduced to other distributed momentum methods, such as the parametric distributed momentum. CDM converges to the optimal solution at a globalR-linear rate for any smooth and strongly convex function when the step-size and momentum coefficient satisfy some bounded conditions. Numerical results for some distributed optimization problems demonstrate that CDM yields a performance that is superior to that of the state-of-the-art methods.