AN ACCELERATED VARIANCE REDUCED EXTRA-POINT APPROACH TO FINITE-SUM HEMIVARIATIONAL INEQUALITY PROBLEM
Journal
SIAM Journal on Optimization
Journal Volume
36
Journal Issue
2
Start Page
1154
End Page
1181
ISSN
10526234
Date Issued
2026
Author(s)
Abstract
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problems. In this HVI problem, the associated function is assumed to be differentiable, and both the vector mapping and the function are of finite-sum structure. We propose two algorithms to solve the cases when the vector mapping is either merely monotone or strongly monotone, while the function is assumed to be convex. We show how to apply variance reduction in the proposed algorithms when such an HVI problem has a finite-sum structure, and the resulting accelerated gradient complexities can match the best bound established for the finite-sum variational inequalities problem, as well as the bound given by the direct Katyusha for finite-sum optimization, respectively, in terms of the corresponding parameters such as (gradient) Lipschitz constants and the sizes of the finite sums. We demonstrate the application of our algorithms through solving a finite-sum constrained finite-sum optimization problem and provide preliminary numerical results.
Subjects
finite-sum optimization
hemivariational inequalities
variance reduction method
variational inequalities
Publisher
Society for Industrial and Applied Mathematics Publications
Type
journal article