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Near-optimal tensor methods for minimizing the gradient norm of convex function | | Pavel Dvurechensky
; Alexander Gasnikov
; Petr Ostroukhov
; César A. Uribe
; Anastasiya Ivanova
; | | Date: |
7 Dec 2019 | | Abstract: | Motivated by convex problems with linear constraints and, in particular, by
entropy-regularized optimal transport, we consider the problem of finding
$varepsilon$-approximate stationary points, i.e. points with the norm of the
objective gradient less than $varepsilon$, of convex functions with Lipschitz
$p$-th order derivatives. Lower complexity bounds for this problem were
recently proposed in [Grapiglia and Nesterov, arXiv:1907.07053]. However, the
methods presented in the same paper do not have optimal complexity bounds. We
propose two optimal up to logarithmic factors methods with complexity bounds
$ ilde{O}(varepsilon^{-2(p+1)/(3p+1)})$ and
$ ilde{O}(varepsilon^{-2/(3p+1)})$ with respect to the initial objective
residual and the distance between the starting point and solution respectively. | | Source: | arXiv, 1912.3381 | | Services: | Forum | Review | PDF | Favorites | |
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