On systems of variational inequalities (Q1282487)

A system of variational inequalities is studied, to find \(\overline u\) in a convex set \(U\), satisfying a system of inequalities \(\langle\overline g_s,u-\overline u\rangle\geq 0\) \((\forall u\in U)\), for \(\overline g_s\in G_s(\overline u)\), for given set-functions \(G_s\). An existence theorem is given, and relations to other variational inequalities are discussed, including lexicographic optimization. An iterative relaxation algorithm is described to solve such systems and a convergence theorem is proved.