This paper investigates the local convergence of the Lagrange–SQP–Newton method applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof converg...

This paper investigates the local convergence of the Lagrange{SQP{Newton method applied to an optimal control problem governed by a phase eld equation with distributed control. The phase eld equation is a system of two semilinear parabolic diierential equations. Stability analysis of optimization problems and regularity results for parabolic diierential equations are used to proof convergence o...

Abstract. An optimal control problem for a parabolic obstacle variational inequality is considered. The obstacle in L 0; T ;H( ) \H 0 ( ) with t 2 L (Q) is taken as the control, and the solution to the obstacle problem taken as the state. The goal is to nd the optimal control so that the state is close to the desired pro le while the norm of the obstacle is not too large. Existence and necessar...

In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

This note summarizes some recent advances on the theory of optimality conditions for PDE optimization. We focus our attention on the concept of strong minima for optimal control problems governed by semi-linear elliptic and parabolic equations. Whereas in the field of calculus of variations this notion has been deeply investigated, the study of strong solutions for optimal control problems of p...

Abstract We present, analyze, and test locally stabilized space–time finite element methods on fully unstructured simplicial meshes for the numerical solution of tracking parabolic optimal control problems with standard L 2 -regularization.We derive a priori discretization error estimates in terms local mesh-sizes shape-regular meshes. The adaptive version is driven by residual indicators, or, ...