Mixed discretization-optimization methods for nonlinear elliptic optimal control problems

Chryssoverghi, I

dc.contributor.author	Chryssoverghi, I	en
dc.date.accessioned	2014-03-01T02:51:07Z
dc.date.available	2014-03-01T02:51:07Z
dc.date.issued	2007	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35384
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-35448984442&partnerID=40&md5=aa38895a2ce171deed434dea041aab5b	en
dc.subject.other	Constraint theory	en
dc.subject.other	Discrete time control systems	en
dc.subject.other	Finite element method	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Continuous classical problems	en
dc.subject.other	Discretization	en
dc.subject.other	Nonlinear elliptic optimal control problems	en
dc.subject.other	Optimization methods	en
dc.subject.other	Partial differential equations	en
dc.title	Mixed discretization-optimization methods for nonlinear elliptic optimal control problems	en
heal.type	conferenceItem	en
heal.publicationDate	2007	en
heal.abstract	An optimal control problem is considered, for systems governed by a nonlinear elliptic partial differential equation, with control and state constraints. Since this problem may have no classical solutions, it is also formulated in the relaxed form. The classical problem is discretized by using a finite element method, where the controls are approximated by elementwise constant, linear, or multilinear, controls. Our first result is that strong accumulation points in L2 of sequences of admissible and extremal discrete controls are admissible and weakly extremal classical for the continuous classical problem, and that relaxed accumulation points of sequences of admissible and extremal discrete controls are admissible and weakly extremal relaxed for the continuous relaxed problem. We then propose a penalized gradient projection method, applied to the discrete problem, and a corresponding discretization-optimization method, applied to the continuous classical problem, that progressively refines the discretization during the iterations, thus reducing computing time and memory. We prove that accumulation points of sequences generated by the first method are admissible and extremal for the discrete problem, and that strong classical (resp. relaxed) accumulation points of sequences of discrete controls generated by the second method are admissible and weakly extremal classical (resp. relaxed) for the continuous classical (resp. relaxed) problem. Finally, numerical examples are given. © Springer-Verlag Berlin Heidelberg 2007.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.volume	4310 LNCS	en
dc.identifier.spage	287	en
dc.identifier.epage	295	en