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Mixed discretization-optimization methods for nonlinear elliptic optimal control problems

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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 http://hdl.handle.net/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


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