5. Variational Inequalities and Mixed Problems
Society for Industrial and Applied Mathematics eBooks · 2011
So far, we have demonstrated the applicability of semismooth Newton methods mainly for the NCP (1.17). We now discuss several applications to more general classes of problems. First, we show how the semismooth reformulation approach that we investigated in detail for the NCP can be extended to the larger problem class of bound-constrained VIPs (1.14). In addition, we describe how semismooth reformulations can be obtained for even more general problems than the bound-constrained VIP. The second extension considers mixed problems consisting of VIPs and additional operator equations. In particular, the first-order necessary (Karush–Kuhn–Tucker, KKT) conditions of very general optimization problems can be written in this form.