On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems. (3rd October 2019)

• Record Type: Journal Article
• Authors: Breitenbach, Tim; Borzì, Alfio
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 13(2019)
• Page Start: 1489
• Page End: 1531
• Publication Date: 2019-10-03
• Subjects: SQH method -- Pontryagin maximum principle -- nonsmooth optimizaiton -- nonconvex optimization; 35J25 -- 35K10 -- 49K20 -- 49M05 -- 65K05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1599911
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of nonsmooth and nonconvex partial differential equation (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, nonconvex, and discontinuous costs of the controls, L 1 tracking terms, and the case of state constraints. The SQH method is based on the characterization 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.