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。