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

Chryssoverghi, I

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