Discretization-optimization methods for relaxed optimal control of nonlinear parabolic systems

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T01:55:23Z
dc.date.available	2014-03-01T01:55:23Z
dc.date.issued	2006	en
dc.identifier.issn	11092769	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27711
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-37849189187&partnerID=40&md5=116468fc1afd3b4ccfc30aad1265dabf	en
dc.subject	Discrete penalized conditional descent method	en
dc.subject	Discretization	en
dc.subject	Finite elements	en
dc.subject	Nonlinear parabolic systems	en
dc.subject	Optimal control	en
dc.subject	Optimality conditions	en
dc.subject	Progressive refining	en
dc.subject	Relaxed controls	en
dc.subject	State constraints	en
dc.subject	Theta-scheme	en
dc.subject.other	Finite element method	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Optimal control systems	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Discretization	en
dc.subject.other	Nonlinear parabolic systems	en
dc.subject.other	Relaxed controls	en
dc.subject.other	State constraints	en
dc.subject.other	Theta-scheme	en
dc.subject.other	Optimization	en
dc.title	Discretization-optimization methods for relaxed optimal control of nonlinear parabolic systems	en
heal.type	journalArticle	en
heal.publicationDate	2006	en
heal.abstract	An optimal control problem is considered, for systems described by a parabolic partial differential equation, jointly nonlinear in the state and control variables, with control and state constraints. Since no convexity assumptions are made on the data, this problem may have no classical solutions, and thus it is reformulated in the relaxed form. The relaxed problem is discretized by using a finite element method in space and an implicit theta-scheme in time, while the controls are approximated by blockwise constant relaxed controls. Necessary and sufficient conditions for optimality are given for the relaxed problem, in the continuous and discrete cases. Results are obtained on the behavior in the limit of discrete optimality, and of discrete admissibility and extremality. In addition, we propose a penalized conditional descent method, applied to the discrete relaxed problem, and a progressively refining version of this method, applied to the continuous relaxed problem, that reduces computing time and memory. The behavior in the limit of sequences constructed by these methods is examined. Finally, numerical examples are given.	en
heal.journalName	WSEAS Transactions on Mathematics	en
dc.identifier.volume	5	en
dc.identifier.issue	11	en
dc.identifier.spage	1153	en
dc.identifier.epage	1160	en