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PreprintCC BY 4.0HAL

Stochastic Model-Based Methods for Minimizing Paraconvex Functions

  • Tan Khiem Huynh
  • Van Ngai Huynh
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Abstract

This paper studies stochastic algorithms for minimizing paraconvex functions, a function class that generalizes weakly convex functions and includes, for instance, Hölder smooth functions and compositions of convex functions with Hölder smooth maps. We first establish the convergence of the stochastic subgradient method and the stochastic proximal subgradient method for unconstrained and composite paraconvex optimization, respectively. The analysis is then extended to a broad family of algorithms that access the objective through stochastic models satisfying certain approximationquality and continuity assumptions. The main principle that underlies the convergence analysis is that the algorithms under consideration can be interpreted as perturbed descent methods on the generalized Moreau envelope of the original paraconvex problem.

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Cite

BibTeXRIS
BibTeX
@misc{huynh2026stochastic,
  title = {{Stochastic Model-Based Methods for Minimizing Paraconvex Functions}},
  author = {Tan Khiem Huynh and Van Ngai Huynh},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35095},
  eprint = {2609.35095},
  archivePrefix = {arXiv},
  url = {https://inria.hal.science/hal-05795150v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stochastic Model-Based Methods for Minimizing Paraconvex Functions
AU  - Tan Khiem Huynh
AU  - Van Ngai Huynh
PY  - 2026
DA  - 2026/09/28
PB  - HAL
DO  - 10.48550/arxiv.2609.35095
UR  - https://inria.hal.science/hal-05795150v1
AB  - This paper studies stochastic algorithms for minimizing paraconvex functions, a function class that generalizes weakly convex functions and includes, for instance, Hölder smooth functions and compositions of convex functions with Hölder smooth maps. We first establish the convergence of the stochastic subgradient method and the stochastic proximal subgradient method for unconstrained and composite paraconvex optimization, respectively. The analysis is then extended to a broad family of algorithms that access the objective through stochastic models satisfying certain approximationquality and continuity assumptions. The main principle that underlies the convergence analysis is that the algorithms under consideration can be interpreted as perturbed descent methods on the generalized Moreau envelope of the original paraconvex problem.
ER  -