In this paper, a new variant of accelerated gradient descent is proposed. The
pro-posed method does not require any information about the objective function,
usesexact line search for the practical accelerations of convergence, converges
accordingto the well-known lower bounds for both convex and non-convex
objective functions,possesses primal-dual properties and can be applied in the
non-euclidian set-up. Asfar as we know this is the rst such method possessing
all of the above properties atthe same time. We also present a universal
version of the method which is applicableto non-smooth problems. We demonstrate
how in practice one can efficiently use thecombination of line-search and
primal-duality by considering a convex optimizationproblem with a simple
structure (for example, linearly constrained).

本文提出一种新的加速梯度下降的变种，该方法不需要任何有关目标函数的信息，使用精确线性搜索进行实际加速收敛，可以根据已知的凸和非凸目标函数的下界进行收敛，具有原始对偶属性，并可在非欧几里得设置中应用。同时，我们还提出了一种适用于非平滑问题的通用方法。

具有小维松弛预测器的原始 - 对偶加速梯度方法

Primal-dual accelerated gradient methods with small-dimensional  relaxation oracle

In this book we collect many different and useful facts around gradient
descent method. First of all we consider gradient descent with inexact oracle.
We build a general model of optimized function that include composite
optimization approach, level's methods, proximal methods etc. Then we
investigate primal-dual properties of the gradient descent in general model
set-up. At the end we generalize method to universal one.

本书集合了很多关于梯度下降方法的不同而有用的知识点，包括带不精确 oracle 的梯度下降法、复合优化方法、proximal 方法，研究它们在普遍模型中的原始 - 对偶属性，最后将方法推广到通用的方法。