A SELF-ADAPTIVE ITERATIVE ALGORITHM FOR SOLVING A CLASS OF BILEVEL SPLIT VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACES

Abstract

The aim of this paper is to examine a complex bilevel problem of finding solutions to multiple sets of variational inequalities in Hilbert spaces. This problem is challenging and requires an effective solution method. We propose a self-adaptive algorithm that dynamically adjusts the step sizes based on the information from the previous step. We rigorously prove the strong convergence of our algorithm and demonstrate that it requires less restrictive conditions than the ones used by Censor et al. (2012). We apply our main results to solve an important problem: the split variational inequality problem. Our analysis shows that our algorithm converges strongly with weaker assumptions than those used recently by Censor et al. (2012) and Buong (2017). To further illustrate the convergence behavior of our method, we provide some numerical examples that demonstrate its effectiveness and efficiency.