algorithms-optimization / Variational inequalities
Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general monotone variational inequalities could be improved was open. A large-step inexact Halpern iteration achieves O(T^-2), and O(T^-p) at pth order.
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Improves every prior result for p >= 2 and matches the classical extragradient method at p = 1.
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Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general monotone variational inequalities could be improved was open. A large-step inexact Halpern iteration achieves O(T^-2), and O(T^-p) at pth order.
Improves every prior result for p >= 2 and matches the classical extragradient method at p = 1.
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