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Approximate gradient/penalty methods with general discretization schemes for optimal control problems

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dc.contributor.author Chryssoverghi, I en
dc.date.accessioned 2014-03-01T02:43:57Z
dc.date.available 2014-03-01T02:43:57Z
dc.date.issued 2006 en
dc.identifier.issn 0302-9743 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/31567
dc.subject.classification Computer Science, Theory & Methods en
dc.subject.other Constraint theory en
dc.subject.other Differential equations en
dc.subject.other Equations of state en
dc.subject.other Gradient methods en
dc.subject.other Polynomial approximation en
dc.subject.other Problem solving en
dc.subject.other Runge Kutta methods en
dc.subject.other Discrete controls en
dc.subject.other Discretization en
dc.subject.other Gradient projection methods en
dc.subject.other Piecewise polynomial functions en
dc.subject.other Optimal control systems en
dc.title Approximate gradient/penalty methods with general discretization schemes for optimal control problems en
heal.type conferenceItem en
heal.identifier.primary 10.1007/11666806_21 en
heal.identifier.secondary http://dx.doi.org/10.1007/11666806_21 en
heal.language English en
heal.publicationDate 2006 en
heal.abstract We consider an optimal control problem described by ordinary differential equations, with control and state constraints. The state equation is first discretized by a general explicit Runge-Kutta scheme and the controls are approximated by piecewise polynomial functions. We then propose approximate gradient and gradient projection methods, and their penalized versions, that construct sequences of discrete controls and progressively refine the discretization during the iterations. Instead of using the exact discrete cost derivative, which usually requires tedious calculations of composite functions, we use here an approximate derivative of the cost defined by discretizing the continuous adjoint equation by the same, but nonmatching, Runge-Kutta scheme backward and the integral involved by a Newton-Cotes integration rule. We show that strong accumulation points in L2 of sequences constructed by these methods satisfy the weak necessary conditions for optimality for the continuous problem. Finally, numerical examples are given. © Springer-Verlag Berlin Heidelberg 2006. en
heal.publisher SPRINGER-VERLAG BERLIN en
heal.journalName Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) en
heal.bookName LECTURE NOTES IN COMPUTER SCIENCE en
dc.identifier.doi 10.1007/11666806_21 en
dc.identifier.isi ISI:000236456400021 en
dc.identifier.volume 3743 LNCS en
dc.identifier.spage 199 en
dc.identifier.epage 207 en


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