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- W2728907422 abstract "The asymptotic convergence rate of iterative algorithms for unconditional optimization in the presence of random noise is studied. The optimal algorithm is found, which maximaze the rate of convergence. The algorithm involves the nonlinear transformation of the gradient; the form of the transformation depends on the density of the noise. To find the best algorithm in the situation when the density is unknown we apply robust estimation ideology. We provide the algorithm which is asimptotically minimax for the specified class of densities. Some examples of the optimal and robust algorithms are presented. The numerical experiments verify the theoretical conclusions; they also demonstrate the difference between the asymptotic and nonasymptotic behavior of the algorithms in some cases." @default.
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- W2728907422 date "1981-08-01" @default.
- W2728907422 modified "2023-09-25" @default.
- W2728907422 title "Optimal and Robust Methods for Unconditional Optimization" @default.
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- W2728907422 doi "https://doi.org/10.1016/s1474-6670(17)63536-5" @default.
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