Bibliographic Details
| Title: |
A SEARCH-FREE O(1/k3/2) HOMOTOPY INEXACT PROXIMAL-NEWTON EXTRAGRADIENT ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITIES. |
| Authors: |
MARQUES ALVES, M.1 maicon.alves@ufsc.br, PEREIRA, J. M.2 jpereira@impa.br, SVAITER, B. F.2 benar@impa.br |
| Source: |
SIAM Journal on Optimization. 2024, Vol. 34 Issue 4, p3235-3258. 24p. |
| Subjects: |
Hilbert space, Algorithms, Variational inequalities (Mathematics) |
| Abstract: |
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/ρ2/3) iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
