Parareal in time intermediate targets methods for optimal control problem

TL;DR

This paper introduces a parallelizable method for solving optimal control problems of parabolic equations by iteratively updating intermediate targets, enabling independent sub-problems to be solved concurrently, and demonstrates its efficiency through numerical experiments.

Contribution

It presents a novel parallel in time approach combining intermediate targets with the parareal algorithm for optimal control of parabolic equations.

Findings

Method achieves efficient parallel computation.

Numerical experiments confirm improved performance.

Applicable to optimal control problems of parabolic PDEs.

Abstract

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.