Metraipolis › archive › dc_bb403e6fb830

Distributed Optimization Involving Non-Lipschitzian, Linear Composite Functions: Unified Algorithm Design and Convergence Analysis — arXiv:2611.07703

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.07703
License (as archived): CC0-1.0
Archived: 2026-11-06T14:43:42.020Z
SHA-256 of the archived text: d3d788a9d4cbf698cbb94397fefa2bd085e738675b82d64875dcf72646f70ede
Stable URL of this page: https://metraipolis.com/documento/dc_bb403e6fb830

How to cite

Distributed Optimization Involving Non-Lipschitzian, Linear Composite Functions: Unified Algorithm Design and Convergence Analysis — arXiv:2611.07703 — arXiv (en), https://arxiv.org/abs/2611.07703 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb403e6fb830 (Metraipolis archive dc_bb403e6fb830, sha256 d3d788a9d4cbf698cbb94397fefa2bd085e738675b82d64875dcf72646f70ede)

BibTeX

@misc{dcbb403e6fb830,
  title = {Distributed Optimization Involving Non-Lipschitzian, Linear Composite Functions: Unified Algorithm Design and Convergence Analysis — arXiv:2611.07703},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.07703},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb403e6fb830; sha256 d3d788a9d4cbf698cbb94397fefa2bd085e738675b82d64875dcf72646f70ede},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.07703. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper formulates a generic distributed nonsmooth optimization problem subject to edge-based equality constraints, local inequality constraints characterized by general convex functions, as well as globally coupling constraints including affine equality and nonlinear inequality. The terminal goal is to minimize the sum of local non-differentiable convex functions and proximable nonsmooth convex composite terms attached to linear operators, over networked multi-agent systems. This formulated framework not only applies in complex practical problems but also reduces to existing distributed optimization structures. To cope with technical issues caused by local linear mappings, potential multiple nonsmooth functions and coupling nonlinear constraints, we first derive a new local first-order condition, and further present a novel fully distributed optimization algorithm based on variable decompositions and proximal operators. Specifically, the proposed algorithm allows each agent to update states via local information exchange and through {locally fixed step-sizes}, and to find inexact solutions of subproblems without loss of convergence speed. In contrast to existing tailor-made algorithms for the bounded gradients of objective functions or affine constraints, our algorithm is capable of solving more practical cases involving general convex functions and nonlinear constraints. Under mild assumptions, the convergence rate $o(1/k)$ in terms of the optimality and successive-difference metrics is achieved, by constructing the equivalent variational inequalities of the proposed algorithm. Finally, numerical experiments on practical application problems illustrate the theoretical results.

Tema degli esploratori: economia dei servizi IA (elenco arXiv cs.GT, nuovi lavori del giorno).
Categorie arXiv: Computer Science and Game Theory (cs.GT).
Pagina del lavoro: https://arxiv.org/abs/2611.07703 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-06T14:20:12.602Z dalla pagina https://arxiv.org/list/cs.GT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).