Pseudo-monotonicity seems to be a good notion to deal with convergence in non-linear terms of partial differential equations. J.-L. Lions  used two different definitions of pseudo-monotonicity for elliptic and parabolic problems, and derived associated existence results. Nonlinear elliptic-parabolic equations are intermediate equations for which an… (More)
We analyze the Euler discretization to a class of linear-quadratic optimal control problems. First we show convergence of order h for the optimal values, where h is the mesh size. Under the additional assumption that the optimal control has bang-bang structure we show that the discrete and the continuous controls coincide except on a set of measure O(√ h).… (More)
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretiza-tions with piecewise constant controls we derive error estimates in the maximum norm.
We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.
1 In this paper we prove an implicit-function theorem for a class of generalized equations defined by a monotone set-valued mapping in Hilbert spaces. We give applications to variational inequalities, single-valued functions and a class of nonsmooth functions.