  This paper investigates a novel approach for solving the distributed
optimization problem in which multiple agents collaborate to find the global
decision that minimizes the sum of their individual cost functions. First, the
$AB$/Push-Pull gradient-based algorithm is considered, which employs row- and
column-stochastic weights simultaneously to track the optimal decision and the
gradient of the global cost function, ensuring consensus on the optimal
decision. Building on this algorithm, we then develop a general algorithm that
incorporates acceleration techniques, such as heavy-ball momentum and Nesterov
momentum, as well as their combination with non-identical momentum parameters.
Previous literature has established the effectiveness of acceleration methods
for various gradient-based distributed algorithms and demonstrated linear
convergence for static directed communication networks. In contrast, we focus
on time-varying directed communication networks and establish linear
convergence of the methods to the optimal solution, when the agents' cost
functions are smooth and strongly convex. Additionally, we provide explicit
bounds for the step-size value and momentum parameters, based on the properties
of the cost functions, the mixing matrices, and the graph connectivity
structures. Our numerical results illustrate the benefits of the proposed
acceleration techniques on the $AB$/Push-Pull algorithm.
