TY  - JOUR
A1  - Breitenbach, Tim
A1  - Borzì, Alfio
T1  - The Pontryagin maximum principle for solving Fokker–Planck optimal control problems
JF  - Computational Optimization and Applications
N2  - The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies.
KW  - Fokker–Planck equation
KW  - Pontryagin maximum principle
KW  - non-smooth optimal control problems
KW  - stochastic processes
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-232665
SN  - 0926-6003
VL  - 76
ER  - 
TY  - INPR
A1  - Breitenbach, Tim
A1  - Borzì, Alfio
T1  - On the SQH scheme to solve non-smooth PDE optimal control problems
T2  - Numerical Functional Analysis and Optimization
N2  - A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints.  

The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin's maximum principle (PMP). For each problem, a theoretical discussion of the PMP optimality condition is given and results of numerical experiments are presented that demonstrate the large range of applicability of the SQH scheme.
KW  - SQH method
KW  - non-smooth optimization
KW  - Pontryagin maximum principle
KW  - nonconvex optimization
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-180936
N1  - This is an Accepted Manuscript of an article published by Taylor & Francis in Numerical Functional Analysis and Optimization on 27.04.2019, available online: http://www.tandfonline.com/10.1080/01630563.2019.1599911.
ER  -