## Abstract

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 <inline-formula><tex-math notation="LaTeX">$AB$</tex-math></inline-formula>/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 <inline-formula><tex-math notation="LaTeX">$AB$</tex-math></inline-formula>/Push-Pull algorithm.

Original language | English (US) |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | IEEE Transactions on Control of Network Systems |

DOIs | |

State | Accepted/In press - 2023 |

Externally published | Yes |

## Keywords

- accelerated algorithm
- Communication networks
- Control systems
- Convergence
- Cost function
- directed graph
- Directed graphs
- Distributed optimization
- Estimation
- Network systems
- time-varying graph

## ASJC Scopus subject areas

- Control and Systems Engineering
- Signal Processing
- Computer Networks and Communications
- Control and Optimization