On new strong convergence result for solving the triple-hierarchical constrained optimization problem

Abstract

This paper introduces a novel generalized iterative algorithm designed to solve the triple-hierarchical constrained optimization problem, which involves a variational inequality defined over the solution set of another variational inequality, constrained by the fixed-point set. Theoretical analysis reveals a strong convergence result for the proposed algorithm, within the rigorous framework of real Hilbert spaces. To illustrate the practical utility and robustness of the algorithm, we present several numerical examples, which not only substantiate the main theoretical results but also highlight the algorithm's capability in addressing complex and structured optimization problems with multiple layers of constraints.