Programming in abstract spaces, Numerical optimization and variational techniques, inner-iterative schemes, convergence, Variational inequalities, Newton-type methods, Kantorovich theorem, generalized equations, nonlinear complementarity, generalized Newton method, nonsmooth equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), variational inequalities