From PDEs constrained optimization to controllability problems via time domain decomposition

TL;DR

This paper explores how time domain decomposition methods can be applied to PDE-constrained optimization and controllability problems, revealing their similar convergence behaviors through theoretical analysis and numerical experiments.

Contribution

It establishes a connection between PDE-constrained optimization and controllability problems and demonstrates the effectiveness of time domain decomposition for both.

Findings

Time domain decomposition leads to similar convergence in both problem types.

Numerical experiments confirm theoretical convergence results.

The link between optimization and controllability problems is clarified.

Abstract

This paper focuses on the application of time domain decomposition to solve partial differential equations constrained optimization problems and controllability problems. After clarifying the link between these two types of problems, we show that applying time domain decomposition to both problems leads to the same convergence behavior. Our numerical experiments also confirm these theoretical findings.