Douglas-Rachford splitting algorithm for projected solution of quasi variational inequality with non-self constraint map

TL;DR

This paper introduces a Douglas-Rachford splitting algorithm designed to find projected solutions for quasi-variational inequalities in Hilbert spaces, leveraging Lipschitz continuity and strong monotonicity of the operator.

Contribution

The paper develops a novel Douglas-Rachford splitting method tailored for quasi-variational inequalities with non-self constraint maps, under specific operator conditions.

Findings

Algorithm converges under Lipschitz and strong monotonicity assumptions.

Provides a new iterative method for quasi-variational inequalities.

Applicable to problems with non-self constraint maps.

Abstract

In this paper, we present a Douglas-Rachford splitting algorithm within a Hilbert space framework that yields a projected solution for a quasi-variational inequality. This is achieved under the conditions that the operator associated with the problem is Lipschitz continuous and strongly monotone. The proposed algorithm is based on the interaction between the resolvent operator and the reflected resolvent operator.