## Abstract

In this article, a distributed optimization problem for minimizing a sum, sum {-{i = 1}-n{f-i}} , of convex objective functions, f_{i}, on directed graph topologies is addressed. Here each function f_{i} is a function of n variables, private to agent i which defines the agent's objective. These f_{i}'s are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant independent of the network size and topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within an O(ρ) neighborhood, where ρ can be chosen to be arbitrarily small.

Original language | English (US) |
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Title of host publication | 2020 American Control Conference, ACC 2020 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4689-4694 |

Number of pages | 6 |

ISBN (Electronic) | 9781538682661 |

DOIs | |

State | Published - Jul 2020 |

Event | 2020 American Control Conference, ACC 2020 - Denver, United States Duration: Jul 1 2020 → Jul 3 2020 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2020-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2020 American Control Conference, ACC 2020 |
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Country/Territory | United States |

City | Denver |

Period | 7/1/20 → 7/3/20 |

### Bibliographical note

Funding Information:This work is supported by Advanced Research Projects Agency-Energy OPEN through the project titled "Rapidly Viable Sustained Grid" via grant no. DE-AR0001016.

Publisher Copyright:

© 2020 AACC.

## Keywords

- Distributed optimization
- distributed gradient descent
- finite-time consensus
- multi-agent networks