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PreprintarXiv licencearXiv

The Method of Ellipcenters for strongly convex minimization

  • Roger Behling
  • Ramyro Correa
  • Eduarda Ferreira
  • Vincent Guigues
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Abstract

This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow capture ill-conditioning of the underlying optimization problem. In the first article on ME, we were able to prove that it converges with linear rate when the objective function is quadratic and strongly convex, while here we derive convergence for any differentiable strongly convex objective. This investigation was inspired by the great performance of ME in quadratic minimization against steepest descent with exact line search, FISTA, Barzilai-Borwein and Conjugate Gradient. The experiments we carry out now, make ME even more attractive from the numerical point of view. On top of that, the theory seems promising for quite more general settings.

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Cite

BibTeXRIS
BibTeX
@misc{behling2026method,
  title = {{The Method of Ellipcenters for strongly convex minimization}},
  author = {Roger Behling and Ramyro Correa and Eduarda Ferreira and Vincent Guigues},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.12820},
  eprint = {2605.12820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.12820},
}
RIS
TY  - UNPB
TI  - The Method of Ellipcenters for strongly convex minimization
AU  - Roger Behling
AU  - Ramyro Correa
AU  - Eduarda Ferreira
AU  - Vincent Guigues
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2605.12820
UR  - https://arxiv.org/abs/2605.12820
AB  - This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow capture ill-conditioning of the underlying optimization problem. In the first article on ME, we were able to prove that it converges with linear rate when the objective function is quadratic and strongly convex, while here we derive convergence for any differentiable strongly convex objective. This investigation was inspired by the great performance of ME in quadratic minimization against steepest descent with exact line search, FISTA, Barzilai-Borwein and Conjugate Gradient. The experiments we carry out now, make ME even more attractive from the numerical point of view. On top of that, the theory seems promising for quite more general settings.
ER  -