Numerics

This chapter introduces the reader to the development of numerical methods for the approximation of variational inequalities (VIs). A variety of modern numerical methods is presented, starting with projection algorithms, moving to proximal schemes (based on the theory of monotone operators) and completing the tour with duality-based schemes. Emphasis is placed not only on both making the reader understand the ideas and motivation behind each method but also on providing detailed and easy to follow proofs of convergence of these methods. The numerical methods are presented for VIs in general form and are illustrated through a fully worked example relating to American or real options.