A SEARCH-FREE O (1/k3/2) HOMOTOPY INEXACT PROXIMAL-NEWTON EXTRAGRADIENT ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITIES

被引：0

作者：

Alves, M. Marques ^{[1
]}

Pereira, J. M. ^{[2
]}

Svaiter, B. F. ^{[2
]}

机构：

[1] Univ Fed Santa Catarina, Dept Matemat, BR-88040900 Florianopolis, Brazil

[2] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil

来源：

SIAM JOURNAL ON OPTIMIZATION | 2024年 / 34卷 / 04期

关键词：

variational inequalities; monotone inclusions; proximal-Newton algorithm; iteration-complexity; ITERATION-COMPLEXITY; CUBIC REGULARIZATION; OPTIMIZATION; ENLARGEMENT;

D O I：

10.1137/23M1593000

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 p > 0, our main algorithm exhibits pointwise O(1/P) and ergodic O(1/p(2/3)) iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes.

引用

页码：3235 / 3258

页数：24