This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such nume...

Reduced order models (ROM) lead to powerful techniques to address computational challenges in PDE-constrained optimization. However, when incorporated within optimization strategies, ROMs are sufficiently accurate only in a restricted zone and thus, need to be systematically updated over the course of the optimization. As an enabling strategy, trust-region methods provide an excellent adaptive ...

Comments from the Editors Jennifer Erway & Stefan M. Wild . . . . . . . . . . . . . . . . . . . . . 1 Article PDE-Constrained Optimization under Uncertainty Drew P. Kouri and Thomas M. Surowiec . . . . . . . . . . . . . . . 1 Bulletin Event Announcements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Book Announcements . . . . . . . . . . . . . . . . . . . . . . . . . ....

Abstract A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on subject where only continuous were considered. Thanks to properly defined function spaces well posed problem obtained from original fully 3D solution then found by PDE-constrained optimization reformulation. domain decomposition strategy...

We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of elliptic optimal control problems. A rigorous multigrid convergence analysis yields level-independent convergence rates. Numerical experiments indicate that the convergence rates are...

In this paper we consider a PDE-constrained optimization problem where an H1 regularization control term is introduced. We address both timeindependent and time-dependent versions. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and preconditioners for the different problems and illustrate their perfor...

Inverse Kohn–Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute construction of empirical exchange–correlation functionals development techniques for density-based embedding. Unlike forward problems, numerical iKS problems ill-posed be unstable. We discuss some fundamental pra...