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Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems

Zamani,Moslem
; 
Abbaszadehpeivasti,Hadi
; 
de Klerk,Etienne
Abstract
In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class of strongly convex-strongly concave saddle-point problems for one iteration. We also investigate the algorithm without strong convexity and we provide some necessary and sufficient conditions under which the gradient descent-ascent enjoys linear convergence.
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Publisher Copyright: © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Date
2024-09-02
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Tilburg University Research Output Collection
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Keywords
Saddle-point problems, Convergence rate, Gradient descent-ascent method, Minimax optimization problem, Performance estimation, Semidefinite programming
Citation
Zamani, M, Abbaszadehpeivasti, H & de Klerk, E 2024, 'Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems', Optimization Methods & Software, vol. 39, no. 5, pp. 967-989. https://doi.org/10.1080/10556788.2024.2360040
URI
https://hdl.handle.net/20.500.14602/81403
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