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Accelerated Regularized Newton Methods for minimizing composite convex functions
时间  Datetime
2017-09-03 09:30 — 10:30 
地点  Venue
Middle Lecture Room
报告人  Speaker
Yurii Nesterov
单位  Affiliation
Universite Catholique de Louvain, Belgium
邀请人  Host
Jinyan Fan
报告摘要  Abstract

In this talk, we present accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is convex and twice differentiable with Holder-continuous Hessian, and the other is a simple closed convex function. For the case in which the Holder parameter $\nu$ is known, we propose methods that take at most $O(1/\epsilon^{1/(2+\nu)})$ iterations to reduce the functional residual below a given precision $\epsilon > 0$. For the general case, in which the parameter is not known, we propose a universal method that ensures the same precision in at most $O(1/\epsilon^{2/[3(1+\nu)]})$ iterations.

These are the first second-order schemes which can automatically adapt to the appropriate level of smoothness of the objective function.

This is a joint work with Geovani Grapiglia, Univeraity of Parana (Brazil).?