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arXiv · 2608.11412

Convex-Concave Interpolation and Application of PEP to Bilinear-Coupled Saddle-Point Problem

Valery Krivchenko·Alexander Gasnikov·Dmitry Kovalev
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Abstract

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.

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Valery Krivchenko, Alexander Gasnikov, Dmitry Kovalev. 2026-08-11. Convex-Concave Interpolation and Application of PEP to Bilinear-Coupled Saddle-Point Problem. https://arxiv.org/abs/2608.11412

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