Adaptive multilevel trust-region methods for time-dependent PDE-constrained optimization (Q2358175)

The problem is to minimize a function \(f=f(y,u)\), depending on a state vector \(y \in Y\) and a control vector \(u \in U_{ad}\), subject to a nonlinear state equation \(C(y,u)=0\) consisting of a system of partial differential equations with certain initial and/or boundary conditions. Optimality conditions are derived, and finite-dimensional approximations are considered by a trust-region method in combination with a conformal discretizations of the given optimization problem on adaptively refined meshes. Different discretizations and solvers for the PDE and its adjoint may be applied. Error estimates are given, and the global convergence of the procedure is considered. Numerical example are provided for a semilinear PDE-constrained control problem.