Skip to content
DraconiticResearch
Search Sources API
186,541 studies31 sourcesUpdated 56 min ago
PreprintarXiv licencearXiv

Retraction-Based Gradient Projection Algorithms on Manifolds

  • Conglong Xu
  • Hao Wu
Open at sourcePDFDOICite

Abstract

We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an application, we use our framework to study the weighted low-rank approximation. We also provide numerical validation of our convergence results on the image completion task.

Related

  1. Recursive Gradient Retraction Methods for Stochastic Nonconvex Optimization on Stiefel Manifolds
    Zhijie Yuan, Lei Sun, Ganzhao Yuan
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  2. Projection-Free Algorithms for Nonsmooth Stochastic Convex-Concave Saddle-Point Problems
    Khanh-Hung Giang-Tran, Soroosh Shafiee
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  3. Strichartz and Spectral Projection Estimates on Asymptotically Conic Manifolds
    Zhexing Zhang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  4. Projection-Free Multi-level Algorithms for Stochastic Constrained Compositional Optimization
    Wei Jiang, Sifan Yang, Wenhao Yang +4
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descent
    Peter Richtárik, Kaja Gruntkowska, Hanmin Li
    arXivPreprintCC0Full textOptimisation & controlStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{xu2026retractionbased,
  title = {{Retraction-Based Gradient Projection Algorithms on Manifolds}},
  author = {Conglong Xu and Hao Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30885},
  eprint = {2609.30885},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30885},
}
RIS
TY  - UNPB
TI  - Retraction-Based Gradient Projection Algorithms on Manifolds
AU  - Conglong Xu
AU  - Hao Wu
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.30885
UR  - https://arxiv.org/abs/2609.30885
AB  - We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an application, we use our framework to study the weighted low-rank approximation. We also provide numerical validation of our convergence results on the image completion task.
ER  -