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PreprintCC BY-NC-ND 4.0arXiv

Dual-Inertial Bregman Methods with Energy-Based Safeguarding

  • Kangming Chen
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Abstract

We develop dual-inertial Bregman proximal methods for convex optimization and analyze their convergence through an exact signed-drift representation. For unrestarted iterations, one-sided directional curvature control yields a last-iterate cO((1+log k)/k2) rate, improving to cO(k−2) under weighted summability. A computable energy-based safeguard guarantees a global cO(N−1) objective-gap bound, counting all proximal oracle calls. Under a stepsize condition and local quadratic growth with suitable kernel regularity, the safeguarded methods restart finitely and eventually converge linearly. Numerical experiments illustrate the methods on entropy regression and nonnegative least squares.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026dualinertial,
  title = {{Dual-Inertial Bregman Methods with Energy-Based Safeguarding}},
  author = {Kangming Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20420},
  eprint = {2610.20420},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20420},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Dual-Inertial Bregman Methods with Energy-Based Safeguarding
AU  - Kangming Chen
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.20420
UR  - https://arxiv.org/abs/2610.20420
AB  - We develop dual-inertial Bregman proximal methods for convex optimization and analyze their convergence through an exact signed-drift representation. For unrestarted iterations, one-sided directional curvature control yields a last-iterate cO((1+log k)/k^2) rate, improving to cO(k^−2) under weighted summability. A computable energy-based safeguard guarantees a global cO(N^−1) objective-gap bound, counting all proximal oracle calls. Under a stepsize condition and local quadratic growth with suitable kernel regularity, the safeguarded methods restart finitely and eventually converge linearly. Numerical experiments illustrate the methods on entropy regression and nonnegative least squares.
ER  -