Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Optimization and Control

arXiv:2210.03947 (math)
[Submitted on 8 Oct 2022 (v1), last revised 1 Sep 2023 (this version, v2)]

Title:Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization

Authors:Xinli Shi, Guanghui Wen, Xinghuo Yu
View PDF
Abstract:This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying (TV) distributed optimization (TVDO). The objective is to minimize the sum of local TV cost functions subject to the possible TV constraints by the coordination of multiple agents in finite time. Specifically, two classes of TVDO are investigated included unconstrained distributed consensus optimization and distributed optimal resource allocation problems (DORAP) with both TV cost functions and coupled equation constraints. For the previous one, based on non-smooth analysis, a continuous-time distributed discontinuous dynamics with FT convergence is proposed based on an extended zero-gradient-sum method with a local auxiliary subsystem. Then, an FT convergent distributed dynamics is further obtained for TV-DORAP by dual transformation. Particularly, the inversion of the cost functions' Hessians is not required in the dual variables' dynamics, while another local optimization needs to be solved to obtain the primal variable at each time instant. Finally, two numerical examples are conducted to verify the proposed algorithms.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2210.03947 [math.OC]
  (or arXiv:2210.03947v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.03947

Submission history

From: Xinli Shi [view email]
[v1] Sat, 8 Oct 2022 07:33:00 UTC (2,653 KB)
[v2] Fri, 1 Sep 2023 13:18:39 UTC (473 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
math.OC
< prev   |   next >
new | recent | 2022-10
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)