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PreprintCC BY 4.0arXiv

Inertial parameterized Douglas-Rachford for generalized DC programming problems

  • Avinash Dixit
  • Pankaj Gautam
  • Sorin-Mihai Grad
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Abstract

We propose two new Douglas-Rachford type algorithms for solving generalized DC programming problems. More precisely, we deal with the minimization of the sum of two possibly nonsmooth convex functions from which a Fréchet differentiable convex function with a Lipschitz continuous gradient is subtracted, in a Hilbertian framework. We introduce an inertial Douglas-Rachford DC algorithm and a parametrized inertial Douglas-Rachford DC algorithm for solving optimization problems of this type, and study their convergence behavior. Numerical experiments illustrate the behavior of the proposed algorithms when solving sparse recovery and robust classification problems, highlighting their superior performance in comparison with their state-of-the-art counterparts.

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Cite

BibTeXRIS
BibTeX
@misc{dixit2026inertial,
  title = {{Inertial parameterized Douglas-Rachford for generalized DC programming problems}},
  author = {Avinash Dixit and Pankaj Gautam and Sorin-Mihai Grad},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11440},
  eprint = {2610.11440},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11440},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inertial parameterized Douglas-Rachford for generalized DC programming problems
AU  - Avinash Dixit
AU  - Pankaj Gautam
AU  - Sorin-Mihai Grad
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11440
UR  - https://arxiv.org/abs/2610.11440
AB  - We propose two new Douglas-Rachford type algorithms for solving generalized DC programming problems. More precisely, we deal with the minimization of the sum of two possibly nonsmooth convex functions from which a Fréchet differentiable convex function with a Lipschitz continuous gradient is subtracted, in a Hilbertian framework. We introduce an inertial Douglas-Rachford DC algorithm and a parametrized inertial Douglas-Rachford DC algorithm for solving optimization problems of this type, and study their convergence behavior. Numerical experiments illustrate the behavior of the proposed algorithms when solving sparse recovery and robust classification problems, highlighting their superior performance in comparison with their state-of-the-art counterparts.
ER  -