Local minimization algorithms for dynamic programming equations

Kalise, Dante; Kr�ner, Axel; Kunisch, Karl

Abstract

© 2016 Society for Industrial and Applied Mathematics. The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible controls. This minimization is often performed by comparison over a finite number of elements of the control set. In this paper we demonstrate the importance of an accurate realization of these minimization problems and propose algorithms by which this can be achieved effectively. The considered class of equations includes nonsmooth control problems with ℓ1-penalization which lead to sparse controls.

Citation

Kalise, D., Kröner, A., & Kunisch, K. (2016). Local minimization algorithms for dynamic programming equations. SIAM Journal on Scientific Computing, 38(3), A1587-A1615. https://doi.org/10.1137/15M1010269

• Journal Article Type: Article
• Acceptance Date: Mar 11, 2016
• Online Publication Date: Jun 1, 2016
• Publication Date: Jun 1, 2016
• Deposit Date: Nov 12, 2019
• Journal: SIAM Journal on Scientific Computing
• Print ISSN: 1064-8275
• Electronic ISSN: 1095-7200
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 3
• Pages: A1587-A1615
• DOI: https://doi.org/10.1137/15M1010269
• Public URL: https://nottingham-repository.worktribe.com/output/3220055