Composite steepest-descent method for the triple hierarchical variational inequalities

Abstract

In this paper, we introduce and analyze a composite steepest-descent algorithm for solving the triple hierarchical variational inequality problem (THVIP) with the constraints of the monotone variational inequality problem
(VIP) and the common fixed point problem of finitely many nonexpansive mappings in a real Hilbert space. The proposed algorithm is based on Korpelevich's extragradient method, hybrid steepest-descent method and Halpern's iteration method. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is established.