Approximation Methods for Nonconvex Parabolic Optimal Control Problems Using Relaxed Controls

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T01:53:38Z
dc.date.available	2014-03-01T01:53:38Z
dc.date.issued	2004	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27084
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-35048851075&partnerID=40&md5=d64347418215b12bb27234079fb5ab82	en
dc.title	Approximation Methods for Nonconvex Parabolic Optimal Control Problems Using Relaxed Controls	en
heal.type	journalArticle	en
heal.publicationDate	2004	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 θ-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. © Springer-Verlag.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.volume	2907	en
dc.identifier.spage	214	en
dc.identifier.epage	221	en