Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation (Q1578502)

This paper discusses the application of the augmented Lagrangian-sequential quadratic programming (SQP) method to optimal control problems with least squares objective function which are governed by the stationary viscous Burgers equation. Section 2 reviews local convergence properties of the augmented Lagrangian-SQP method in Hilbert space. Sections 3 and 4 are concerned with distributed and Neumann boundary control problems, respectively. Existence of a solution to the optimal control problems are proven, first order necessary optimality conditions are established, and second order sufficient optimality conditions are shown under the assumption that the least squares residual at the solution is sufficiently small (in case of a Neumann boundary control and \(L^2\) observations one also needs a condition on the viscosity parameter). In the final section, a finite element discretization using piecewise linear elements is discussed. Mesh independent convergence of the augmented Lagrangian-SQP method is proven and demonstrated numerically.