A distributed gradient algorithm based on randomized block-coordinate and projection-free over networks

Abstract The computational bottleneck in distributed optimization methods, which is based on projected gradient descent, due to the computation of a full vector and projection step. This particular problem for large datasets. To reduce complexity existing we combine randomized block-coordinate descent Frank–Wolfe techniques, then propose projection-free algorithm over networks, where each agent randomly chooses subset coordinates its step eschewed favor much simpler linear Moreover, convergence performance proposed also theoretically analyzed. Specifically, rigorously prove that can converge optimal point at rate $${\mathcal {O}}(1/t)$$ O ( 1 / t ) under convexity {O}}(1/t^2)$$ 2 strong convexity, respectively. Here, t number iterations. Furthermore, stationary point, “Frank-Wolfe” gap equal zero, {O}}(1/\sqrt{t})$$ non-convexity. evaluate benefit algorithm, use solve multiclass classification problems by simulation experiments two datasets, i.e., aloi news20. results shows faster than algorithms lower per iteration. show well-connected graphs or smaller leads rate, confirm theoretical results.