We propose a new primal-dual algorithmic framework for a prototypical
constrained convex optimization template. The algorithmic instances of our
framework are universal since they can automatically adapt to the unknown
Holder continuity degree and constant within the dual formulation. They are
also guaran- teed to have optimal convergence rates in the objective residual
and the feasibility gap for each Holder smoothness degree. In contrast to
existing primal-dual algorithms, our framework avoids the proximity operator of
the objective function. We instead leverage computationally cheaper,
Fenchel-type operators, which are the main workhorses of the generalized
conditional gradient (GCG)-type methods. In contrast to the GCG-type methods,
our framework does not require the objective function to be differentiable, and
can also process additional general linear inclusion constraints, while
guarantees the convergence rate on the primal problem

提出一种新的原始对偶算法框架，以解决约束的凸优化问题，具有优秀的收敛速度和更高效的计算方式。

一种通用的原始 - 对偶凸优化框架

A Universal Primal-Dual Convex Optimization Framework

In this paper we consider iterative methods for stochastic variational
inequalities (s.v.i.) with monotone operators. Our basic assumption is that the
operator possesses both smooth and nonsmooth components. Further, only noisy
observations of the problem data are available. We develop a novel Stochastic
Mirror-Prox (SMP) algorithm for solving s.v.i. and show that with the
convenient stepsize strategy it attains the optimal rates of convergence with
respect to the problem parameters. We apply the SMP algorithm to Stochastic
composite minimization and describe particular applications to Stochastic
Semidefinite Feasability problem and Eigenvalue minimization.

本文提出了一种新的随机镜子代理（SMP）算法，通过便捷的步长策略优化收敛率，应用于解决了随机组合最小化和特定应用于随机半定可行性问题和最小化特征值的随机变分不等式问题