Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems

Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems

In this article, we motivate, derive and test effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two different functionals, and the Neumann boundary control problem involving Poisson’s equation and the heat e...

Block-triangular preconditioners for PDE-constrained optimization

”Parareal” Time-Domain Decomposition for Time-dependent PDE-constrained Optimization

Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems

We consider large scale sparse linear systems in saddle point form. A natural property of such indefinite 2-by-2 block systems is the positivity of the (1,1) block on the kernel of the (2,1) block. Many solution methods, however, require that the positivity of the (1,1) block is satisfied everywhere. To enforce the positivity everywhere, an augmented Lagrangian approach is usually chosen. Howev...

Pseudo-Time Methods for Constrained Optimization Problems Governed by PDE

In this paper we present a novel method for solving optimization problems governed by partial di erential equations. Existing methods use gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurf...