For deriving error bounds or estimating convergence rates,the classical numerical analysis extensively uses the Taylorexpansion. I will talk about variational problems with constraints to which, as a rule, Taylor's theorem cannot be applied. First, a"neoclassical" interpolation problem will be discussed: find a convex function which interpolates given points and has a minimal L2 norm of the second derivative; by duality this problem reduces to a system of equations involving nonsmooth functions. A Newton-type methodfor this system was proposed in 1985 but its quadratic convergence was provedonly recently.
Next, a Runge-Kutta approximation to a boundary-value problem coupledwith a variational inequality is considered. Tight error bounds will bepresented depending on the regularity of the solution. The third topic is aboutconditioning of systems of inequalities and variational inequalities. I will show that Renegar's distance to infeasibility is equal to the reciprocal of the modulusof metric regularity.