递增梯度、次梯度和近端方法用于凸优化：综述
Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization: A Survey
AI总结：
本文综述了用于最小化大量凸函数和的递增方法，提出了一种统一框架，涵盖梯度、次梯度及新近端方法，分析了收敛性和速率，并讨论了在推断/机器学习、信号处理和大规模分布式优化中的应用。
摘要：
我们综述了用于最小化由大量凸组件函数组成的和的递增方法。这些方法通过单个组件迭代实现，实践中效果显著。我们提出了一种统一的算法框架，涵盖梯度和次梯度迭代，以及结合次梯度和近端方法的新方法，提供了更灵活的特殊结构利用。我们分析了这些方法的收敛性和收敛速率特性，包括随机选择组件带来的优势。此外，我们还综述了在推断/机器学习、信号处理和大规模分布式优化中的应用。
英文摘要：
We survey incremental methods for minimizing a sum $\sum_{i=1}^mf_i(x)$ consisting of a large number of convex component functions $f_i$. Our methods consist of iterations applied to single components, and have proved very effective in practice. We introduce a unified algorithmic framework for a variety of such methods, some involving gradient and subgradient iterations, which are known, and some involving combinations of subgradient and proximal methods, which are new and offer greater flexibility in exploiting the special structure of $f_i$. We provide an analysis of the convergence and rate of convergence properties of these methods, including the advantages offered by randomization in the selection of components. We also survey applications in inference/machine learning, signal processing, and large-scale and distributed optimization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
