Optimization problems subject to constraints given by partial differential equations (PDEs) with additional constraints on the control and/or state variables belong to the most challenging problem classes in natural sciences, engineering, and economics. Due to the complexities of the PDEs and the requirement for rapid solution pose significant challenges for the computational scientists. A part...

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...

In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints bilateral constraints. The approach employs successively enriched Reduced Basis surrogate models that are constructed during the outer loop used as model function method. Each sub-problem is solved projected BFGS Moreover, a non-conforming dual (NC...

We suggest an algorithm for the calculation of large-amplitude traveling water waves in irrotational flows and in flows with constant and nonconstant vorticity, respectively. The algorithm is based on a quite general partial differential equation constrained optimization formulation, maximizing the wave amplitude subject to the PDE constraint that the Euler equations hold. Numerical examples il...

The solution of time-dependent PDE-constrained optimization problems subject to unsteady flow equations presents a challenge to both algorithms and computers. In this paper we present an all-at-once approach where we solve for all time-steps of the discretized unsteady Stokes problem at once. The most desirable feature of this approach is that for all steps of an iterative scheme we only need a...

We introduce a general methodology for parameter identification in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. A quadratic cost functional that measures t...

We investigate an iterative method for the solution of time-periodic parabolic PDE constrained optimization problems. It is an inexact Sequential Quadratic Programming (iSQP) method based on the Newton-Picard approach. We present and analyze a linear quadratic model problem and prove optimal mesh-independent convergence rates. Additionally, we propose a two-grid variant of the Newton-Picard met...

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves res...

9:15 9:30 Opening 9:30 10:30 John A. Burns Sensitivity Analysis, Transition to Turbulence and Control 10:30 11:00 Coffee Break 11:00 12:00 Rainer Tichatschke Bregman-function-based regularization of variational inequalities with monotone operators 12:00 13:00 Lunch Break 13:00 14:00 Stefan Ulbrich Parallel All-at-Once methods with ”Parareal” time-domain decomposition for time-dependent PDE-cons...

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained opt...