Geodesic
Convex-Concave Interpolation and Application of PEP to the Bilinear-Coupled Saddle Point Problem
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 5, pp. 875-893

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In this paper we present interpolation conditions for several important convex-concave function classes: nonsmooth convex-concave functions, conditions for difference of strongly-convex functions in a form that contains oracle information exclusively and smooth convex-concave functions with a bilinear coupling term. Then we demonstrate how the performance estimation problem approach can be adapted to analyze the exact worst-case convergence behavior of first-order methods applied to composite bilinear-coupled min-max problems. Using the performance estimation problem approach, we estimate iteration complexities for several first-order fixed-step methods, Sim-GDA and Alt-GDA, which are applied to smooth convex-concave functions with a bilinear coupling term.
Keywords: saddle point, convex-concave functions, bilinear coupling, performance estimation problem
Mots-clés : interpolation conditions 
@article{ND_2024_20_5_a10,
     author = {V. O. Krivchenko and A. V. Gasnikov and D. A. Kovalev},
     title = {Convex-Concave {Interpolation} and {Application} of {PEP} to the {Bilinear-Coupled} {Saddle} {Point}  {Problem}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {875--893},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2024_20_5_a10/}
}
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V. O. Krivchenko; A. V. Gasnikov; D. A. Kovalev. Convex-Concave Interpolation and Application of PEP to the Bilinear-Coupled Saddle Point  Problem. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 5, pp. 875-893. http://geodesic.mathdoc.fr/item/ND_2024_20_5_a10/