On the relaxation gap for PDE mixed-integer optimal control problems

• Published in: Proceedings in applied mathematics and mechanics Vol. 16; no. 1; pp. 783 - 784
• Main Author: Hante, Falk M.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01-10-2016; WILEY‐VCH Verlag
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201610380

Mixed‐integer optimal control problems require taking discrete and continuous control decisions for the optimization of a dynamical system. We consider dynamics governed by partial differential equations of evolution type and assess the problem by relaxation and rounding strategies. For this solution approach, we present a priori estimates for semilinear evolutions on Banach spaces concerning the optimality gap. The theoretical results show that the gap can be made arbitrary small. We demonstrate the numerical performance of the approach on benchmark problems of parabolic type motivated from thermal manufacturing and of hyperbolic type motivated from traffic flow control. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)