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PreprintCC BY 4.0arXiv

Decentralized Optimization with Cross-Coupled Mixed Affine Constraints

  • Ewsey Obzherin
  • Ilya Khomchenko
  • Natalia Shelegeda
  • Nhat Trung Nguyen
  • Demyan Yarmoshik
  • Alexander Rogozin
  • Alexander Gasnikov
Open at sourcePDFDOICite

Abstract

We study decentralized optimization with cross-coupled mixed affine constraints, where local and shared variables interact through two affine channels. We show that the intrinsic difficulty of combining separately well-conditioned channels is governed by their Friedrichs angle. This geometry induces a cross-coupling factor that cannot be removed by channelwise preconditioning and governs the additional affine-oracle and communication complexity. We develop an accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime and extend the framework to smooth and nonsmooth convex objectives. Experiments confirm the predicted dependence on cross-channel geometry and network conditioning.

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Cite

BibTeXRIS
BibTeX
@misc{obzherin2026decentralized,
  title = {{Decentralized Optimization with Cross-Coupled Mixed Affine Constraints}},
  author = {Ewsey Obzherin and Ilya Khomchenko and Natalia Shelegeda and Nhat Trung Nguyen and Demyan Yarmoshik and Alexander Rogozin and Alexander Gasnikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33021},
  eprint = {2609.33021},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33021},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Decentralized Optimization with Cross-Coupled Mixed Affine Constraints
AU  - Ewsey Obzherin
AU  - Ilya Khomchenko
AU  - Natalia Shelegeda
AU  - Nhat Trung Nguyen
AU  - Demyan Yarmoshik
AU  - Alexander Rogozin
AU  - Alexander Gasnikov
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.33021
UR  - https://arxiv.org/abs/2609.33021
AB  - We study decentralized optimization with cross-coupled mixed affine constraints, where local and shared variables interact through two affine channels. We show that the intrinsic difficulty of combining separately well-conditioned channels is governed by their Friedrichs angle. This geometry induces a cross-coupling factor that cannot be removed by channelwise preconditioning and governs the additional affine-oracle and communication complexity. We develop an accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime and extend the framework to smooth and nonsmooth convex objectives. Experiments confirm the predicted dependence on cross-channel geometry and network conditioning.
ER  -