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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Pogu, M., Souza De Cursi, J.E. Global optimization by random perturbation of the gradient method with a fixed parameter. J Glob Optim 5, 159–180 (1994). https://doi.org/10.1007/BF01100691
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DOI: https://doi.org/10.1007/BF01100691