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A search-free O(1/k^(3/2)) homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities
M. Marques Alves, João M. Pereira, Benar F. Svaiter
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We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance ρ>0, our main algorithm exhibits pointwise O(1/ρ) and ergodic O(1/(ρ^(2/3))) iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes.
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