Solving strongly monotone variational and quasi-variational inequalities

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A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, methodology): “However, this analysis is suboptimal as Nesterov and Scrimali (2006) showed that extragradient converges at a rate of 1 − µ/ (2 L ) in this setting. cover Our analysis builds on the results from Tseng (1995) and extends them to the whole range of games and recover the optimal rate of Nesterov and…”
A Tight and Unified Analysis of Gradient-Based Methods for a Whole Spectrum of Differentiable Games (2020, methodology): “This point of view was presented by Polyak (1987); Bertsekas (1999) and recently used by Arjevani et al.”
Global Convergence and Variance-Reduced Optimization for a Class of Nonconvex-Nonconcave Minimax Problems (2020, methodology): “…/(cid:15) )) iteration complexity (see, e.g., Facchinei and Pang [2007]) and this can be further improved to O ( κ log(1 /(cid:15) )) by extragradient methods [Korpelevich, 1976], Nesterov’s dual extrapolation [Nesterov and Scrimali, 2006] or accelerated proximal point algorithm [Lin et al., 2020].”
Solving Weakly-Convex-Weakly-Concave Saddle-Point Problems as Successive Strongly Monotone Variational Inequalities (2018, methodology): “Remark: In the appendix, we present a variant based on Nesterov’s accelerated method (with two gradient updates at each iteration) [56], which can improve the above complexity when the condition number L/ρ≫ 1 is large.”