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Peer-reviewedCC BY-NC-ND 4.0Journal of Global Optimization

Global optimization by random perturbation of the gradient method with a fixed parameter

  • Marc Pogu
  • José Souza de Cursi
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Abstract

The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method.

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Cite

BibTeXRIS
BibTeX
@article{pogu2026global,
  title = {{Global optimization by random perturbation of the gradient method with a fixed parameter}},
  author = {Marc Pogu and José Souza de Cursi},
  journal = {Journal of Global Optimization},
  year = {2026},
  month = oct,
  doi = {10.1007/bf01100691},
  url = {https://hal.science/hal-05791640v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - JOUR
TI  - Global optimization by random perturbation of the gradient method with a fixed parameter
AU  - Marc Pogu
AU  - José Souza de Cursi
PY  - 2026
DA  - 2026/10/12
JO  - Journal of Global Optimization
DO  - 10.1007/bf01100691
UR  - https://hal.science/hal-05791640v1
AB  - The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method.
SN  - 0925-5001
SN  - 1573-2916
ER  -