Approximation methods for nonconvex parabolic optimal control problems using relaxed controls

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T01:18:41Z
dc.date.available	2014-03-01T01:18:41Z
dc.date.issued	2003	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15152
dc.subject	Approximation Method	en
dc.subject	Distributed Control	en
dc.subject	Finite Element Method	en
dc.subject	Optimal Control Problem	en
dc.subject	Parabolic Partial Differential Equation	en
dc.subject	Penalty Method	en
dc.subject	State Constraints	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	DISCRETE APPROXIMATION	en
dc.subject.other	DESCENT	en
dc.title	Approximation methods for nonconvex parabolic optimal control problems using relaxed controls	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/978-3-540-24588-9_23	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-540-24588-9_23	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	We consider an optimal distributed control problem involving semilinear parabolic partial differential equations, with control and state constraints. Since no convexity assumptions are made, the problem is reformulated in relaxed form. The state equation is discretized using a finite element method in space and a theta-scheme in time, while the controls are approximated by blockwise constant relaxed controls. The first result is that, under appropriate assumptions, the properties of optimality, and of extremality and admissibility, carry over in the limit to the corresponding properties for the relaxed continuous problem. We also propose progressively refining discrete conditional gradient and gradient-penalty methods, which generate relaxed controls, for solving the continuous relaxed problem, thus reducing computations and memory. Numerical examples are given.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	LARGE-SCALE SCIENTIFIC COMPUTING	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/978-3-540-24588-9_23	en
dc.identifier.isi	ISI:000189446500023	en
dc.identifier.volume	2907	en
dc.identifier.spage	214	en
dc.identifier.epage	221	en