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On the relaxation gap for PDE mixed‐integer optimal control problems
Author(s) -
Hante Falk M.
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610380
Subject(s) - rounding , relaxation (psychology) , optimal control , benchmark (surveying) , integer (computer science) , mathematics , type (biology) , partial differential equation , mathematical optimization , a priori and a posteriori , optimization problem , mathematical analysis , computer science , psychology , social psychology , ecology , philosophy , geodesy , biology , programming language , geography , operating system , epistemology
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)