Metraipolis › archive › dc_ec2d33fd36ff

Projection-Free Gradient Tracking Neurodynamic for Distributed Nonnegative Sparse Optimization — arXiv:2611.07643

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.07643
License (as archived): CC0-1.0
Archived: 2026-11-06T14:51:58.834Z
SHA-256 of the archived text: 6bcb7288202a60c65ce66382ef157ad2cae48900838386c41b2d9572fe876811
Stable URL of this page: https://metraipolis.com/documento/dc_ec2d33fd36ff

How to cite

Projection-Free Gradient Tracking Neurodynamic for Distributed Nonnegative Sparse Optimization — arXiv:2611.07643 — arXiv (en), https://arxiv.org/abs/2611.07643 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ec2d33fd36ff (Metraipolis archive dc_ec2d33fd36ff, sha256 6bcb7288202a60c65ce66382ef157ad2cae48900838386c41b2d9572fe876811)

BibTeX

@misc{dcec2d33fd36ff,
  title = {Projection-Free Gradient Tracking Neurodynamic for Distributed Nonnegative Sparse Optimization — arXiv:2611.07643},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.07643},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ec2d33fd36ff; sha256 6bcb7288202a60c65ce66382ef157ad2cae48900838386c41b2d9572fe876811},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.07643. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper proposes a continuous-time, projection-free neurodynamic system based on gradient tracking for distributed nonnegative sparse optimization. Unlike traditional methods, our approach avoids projecting states onto the feasible set. Instead, it employs gradient tracking to estimate average gradients under heterogeneous costs, coupling primal and dual dynamics such that feasibility and sparsity emerge naturally from the equilibrium conditions. The system ensures unique solutions through a locally Lipschitz vector field and guarantees that every equilibrium corresponds to an exact KKT point. We establish rigorous convergence guarantees for convex objectives through three distinct analytical layers. These include a centralized kernel rate, a computable distributed rate derived from Jacobian analysis without restrictive stability assumptions, and a global exponential stability proof based on Lur'e system theory. Our analysis quantitatively separates these layers, revealing that the convergence rate is primarily limited by graph sparsity and remains robust to variations in momentum time scales. Numerical experiments on strongly convex quadratic problems validate the theoretical rates, demonstrate effective active set recovery, and show that the system maintains stable tail convergence rates even under strong local heterogeneity.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC) ; Neural and Evolutionary Computing (cs.NE).
Pagina del lavoro: https://arxiv.org/abs/2611.07643 — 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 2026-11-06T14:23:27.648Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).