A Low-Rank in Time Approach to PDE-Constrained Optimization

A Low-Rank in Time Approach to PDE-Constrained Optimization

The solution of time-dependent PDE-constrained optimization problems is a challenging task in numerical analysis and applied mathematics. All-at-once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder...

A Phase Field Based Pde Constrained Optimization Approach to Time Discrete Willmore Flow

A novel phase field model for Willmore flow is proposed based on a nested variational time discretization. Thereby, the mean curvature in the Willmore functional is replaced by an approximate speed of mean curvature motion, which is computed via a fully implicit variational model for time discrete mean curvature motion. The time discretization of Willmore flow is then performed in a nested fash...

A Rank-Constrained Optimization Approach: Application to Factor Analysis

In this paper, we present a general method for rank-constrained optimization. We use an iterative convex optimization procedure where it is possible to include any extra convex constraints. The proposed approach has potential application in several areas. We focus on the problem of Factor Analysis. In this case, our approach provides sufficient flexibility to handle correlated errors. The benef...

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

Domain decomposition in time for PDE-constrained optimization

PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal ...