PEPit：用 Python 对一阶优化方法进行计算机辅助最坏情况分析
PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python
AI总结：
本文介绍 Python 软件包 PEPit，它通过将性能估计问题自动建模为 SDP，使用户只需按实现形式编写一阶方法，即可借助标准求解器完成计算机辅助最坏情况分析。
摘要：
PEPit 是一个 Python 软件包，旨在简化对一大类一阶优化方法的最坏情况分析；这些方法可能涉及梯度、投影、近端或线性优化预言机，以及它们的近似变体或 Bregman 变体。简而言之，PEPit 是一个能够对一阶优化方法进行计算机辅助最坏情况分析的软件包。其核心思想是将执行最坏情况分析的问题（通常称为性能估计问题，即 PEP）转化为一个可通过数值方式求解的半定规划（SDP）。为此，软件包用户只需按照几乎与实际实现相同的方式编写一阶优化方法。随后，该软件包会处理 SDP 建模部分，并通过标准求解器以数值方式完成最坏情况分析。
英文摘要：
PEPit is a Python package aiming at simplifying the access to worst-case analyses of a large family of first-order optimization methods possibly involving gradient, projection, proximal, or linear optimization oracles, along with their approximate, or Bregman variants. In short, PEPit is a package enabling computer-assisted worst-case analyses of first-order optimization methods. The key underlying idea is to cast the problem of performing a worst-case analysis, often referred to as a performance estimation problem (PEP), as a semidefinite program (SDP) which can be solved numerically. To do that, the package users are only required to write first-order methods nearly as they would have implemented them. The package then takes care of the SDP modeling parts, and the worst-case analysis is performed numerically via a standard solver.
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。
