AI 中文总结
本文研究凸-凹插值，给出凸-凹、双线性及带双线性耦合的复合函数的插值条件，并针对复合鞍点问题的一阶方法构造性能估计问题（PEP），将算法最坏性能求解转化为优化问题。
AI 中文摘要
性能估计问题（PEP）方法将算法精确最坏情况性能的求解重构为优化问题的解，该问题的可处理公式化需要充要插值条件。我们给出凸-凹函数、双线性函数及带双线性耦合的复合函数的插值条件，还针对复合鞍点问题的一阶方法构造了PEP。
英文摘要
The Performance estimation problem (PEP) approach reformulates finding the exact worst-case performance of an algorithm as the solution to an optimization problem. Tractable formulation of the problem requires necessary and sufficient interpolation conditions. We present the interpolation conditions for convex--concave functions, bilinear functions, and composite functions with bilinear coupling. We also construct PEP for first-order methods for composite saddle-point problem.
CommentsThis version revises and extends the paper published in Russian Journal of Nonlinear Dynamics (2024). It expands the section dedicated to construction of PEP for composite saddle-point problems. It focuses strictly on theoretical results, omitting the preliminary numerical data from the journal version
Journal refConvex--concave interpolation and application of PEP to the bilinear-coupled saddle point problem // Russian Journal of Nonlinear Dynamics. 2024. Vol. 20, No. 5. P. 875-893
