Primal Subgradient Methods with Predefined Step Sizes
本文提出分析非光滑凸优化原始次梯度方法的新框架，修正了经典步长规则在约束问题中的不足，并利用目标函数的平滑性和强凸性加速算法，还可近似最优拉格朗日乘子。
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on knowledge of the optimal value of the objective function, need corrections when they are applied to optimization problems with constraints. Their proper modifications allow a significant acceleration of these schemes when the objective function has favorable properties (smoothness, strong convexity). We show how the new methods can be used for solving optimization problems with functional constraints with a possibility to approximate the optimal Lagrange multipliers. One of our primal-dual methods works also for unbounded feasible set.