Classical and relaxed optimization methods for nonlinear parabolic optimal control problems

Chryssoverghi, I; Coletsos, J; Kokkinis, B

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Coletsos, J	en
dc.contributor.author	Kokkinis, B	en
dc.date.accessioned	2014-03-01T02:52:36Z
dc.date.available	2014-03-01T02:52:36Z
dc.date.issued	2010	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35951
dc.subject.other	Classical control	en
dc.subject.other	Descent method	en
dc.subject.other	Distributed optimal control problems	en
dc.subject.other	Gradient projection methods	en
dc.subject.other	Numerical example	en
dc.subject.other	Numerical solution	en
dc.subject.other	Optimal control problem	en
dc.subject.other	Optimality	en
dc.subject.other	Optimization method	en
dc.subject.other	Parabolic partial differential equations	en
dc.subject.other	Relaxation theory	en
dc.subject.other	Relaxed control	en
dc.subject.other	State constraints	en
dc.subject.other	State equations	en
dc.subject.other	Control	en
dc.subject.other	Differential equations	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Numerical methods	en
dc.subject.other	Optimization	en
dc.subject.other	Nonlinear equations	en
dc.title	Classical and relaxed optimization methods for nonlinear parabolic optimal control problems	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-12535-5_28	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-12535-5_28	en
heal.publicationDate	2010	en
heal.abstract	A distributed optimal control problem is considered, for systems defined by parabolic partial differential equations. The state equations are nonlinear w.r.t. the state and the control, and the state constraints and cost depend also on the state gradient. The problem is first formulated in the classical and in the relaxed form. Various necessary conditions for optimality are given for both problems. Two methods are then proposed for the numerical solution of these problems. The first is a penalized gradient projection method generating classical controls, and the second is a penalized conditional descent method generating relaxed controls. Using relaxation theory, the behavior in the limit of sequences constructed by these methods is examined. Finally, numerical examples are given. © 2010 Springer-Verlag Berlin Heidelberg.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-12535-5_28	en
dc.identifier.volume	5910 LNCS	en
dc.identifier.spage	247	en
dc.identifier.epage	255	en