Explicit stabilized integrators for stiff optimal control problems

TL;DR

This paper introduces explicit stabilized integrators of orders one and two for efficiently solving stiff optimal control problems, leveraging their stability and convergence properties demonstrated through numerical experiments.

Contribution

The authors develop and analyze explicit stabilized integrators tailored for stiff optimal control systems, offering an efficient alternative to implicit methods.

Findings

Explicit stabilized integrators exhibit favorable stability properties.

The methods achieve expected order of convergence.

Numerical experiments confirm efficiency in PDE optimal control.

Abstract

Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and two for the optimal control of stiff systems. We analyze their favorable stability properties based on the continuous optimality conditions. Furthermore, we study their order of convergence taking advantage of the symplecticity of the corresponding partitioned Runge-Kutta method involved for the adjoint equations. Numerical experiments including the optimal control of a nonlinear diffusion-advection PDE illustrate the efficiency of the new approach.