论文标题
最大结构非凸优化的原始双重平滑框架
A Primal-Dual Smoothing Framework for Max-Structured Non-Convex Optimization
论文作者
论文摘要
我们提出了一个原始的双重平滑框架，用于查找一类非平滑非平滑非凸优化问题的近乎平稳的点。我们通过两种方法，即双重和原始的双平滑方法分析了框架的原始梯度复杂性。即使在受限的问题设置中，我们的框架也改善了现有方法的最著名的甲骨文复杂性。作为我们框架的重要组成部分，我们提出了一种一阶方法，用于解决一类（强）凸出的凸出鞍点问题，该方法基于一种新开发的非高伯尔伯省非乳酸不精性的近端梯度算法，用于强烈凸起的综合最小化，以享受Duality-a-duality-gap convergence convergence convergence convergence convergence convergence。还讨论了我们框架的一些变体和扩展。
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two approaches, i.e., the dual-then-primal and primal-the-dual smoothing approaches. Our framework improves the best-known oracle complexities of the existing method, even in the restricted problem setting. As an important part of our framework, we propose a first-order method for solving a class of (strongly) convex-concave saddle-point problems, which is based on a newly developed non-Hilbertian inexact accelerated proximal gradient algorithm for strongly convex composite minimization that enjoys duality-gap convergence guarantees. Some variants and extensions of our framework are also discussed.
