论文标题
基于撤回的直接搜索方法，用于衍生的免费riemannian优化
Retraction based Direct Search Methods for Derivative Free Riemannian Optimization
论文作者
论文摘要
直接搜索方法代表了一种可靠的算法类别，用于解决黑框优化问题。 在本文中，我们探讨了这些策略在Riemannian优化中的应用，其中应相对于仅限于歧管的变量进行最小化。更具体地说，我们考虑了经典和线条搜索的直接搜索的推断变体，并且通过使用缩回，我们设计了量身定制的策略，以最大程度地减少平滑和非平滑功能。 因此，我们在文献中首次分析了一类基于缩回的算法，以最大程度地减少Riemannian歧管上的非平滑目标，而无需访问（sub）衍生物。除了融合的保证外，我们还提供了一组标准问题的数值绩效插图。
Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be performed with respect to variables restricted to lie on a manifold. More specifically, we consider classic and line search extrapolated variants of direct search, and, by making use of retractions, we devise tailored strategies for the minimization of both smooth and nonsmooth functions. As such we analyze, for the first time in the literature, a class of retraction based algorithms for minimizing nonsmooth objectives on a Riemannian manifold without having access to (sub)derivatives. Along with convergence guarantees we provide a set of numerical performance illustrations on a standard set of problems.
