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. For doing 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 modelling parts, and the worst-case analysis is performed numerically via a standard solver.
翻译:Python软件包旨在简化对一大批一阶优化方法进行最坏情况分析的机会,这些方法可能涉及梯度、投影、准度、线性优化或触角及其近似值或Bregman变体。简而言之,Python软件包旨在简化对一阶优化方法进行最坏情况分析的机会。关键的基本想法是将进行最坏情况分析(通常被称为绩效估计问题)作为半无限期程序(SDP)的问题,可以用数字方式解决。为此,包用户只需几乎按其实际应用程度编写第一阶方法。包件随后将照顾SDP模型部分,而最坏情况分析则通过标准求解器进行数字分析。