Approximate gradient projection method with Runge-Kutta schemes for optimal control problems

Chryssoverghi, I; Coletsos, J; Kokkinis, B

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Coletsos, J	en
dc.contributor.author	Kokkinis, B	en
dc.date.accessioned	2014-03-01T01:19:55Z
dc.date.available	2014-03-01T01:19:55Z
dc.date.issued	2004	en
dc.identifier.issn	0926-6003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15771
dc.subject	Discretization	en
dc.subject	Gradient projection method	en
dc.subject	Non-matching Runge-Kutta schemes	en
dc.subject	Optimal control	en
dc.subject	Piecewise affine controls	en
dc.subject.classification	Operations Research & Management Science	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Discretization	en
dc.subject.other	Gradient projection methods	en
dc.subject.other	Non-matching Runge-Kutta schemes	en
dc.subject.other	Optimal control	en
dc.subject.other	Piecewise affine controls	en
dc.subject.other	Gradient methods	en
dc.subject.other	Numerical methods	en
dc.subject.other	Optimization	en
dc.subject.other	Problem solving	en
dc.subject.other	Runge Kutta methods	en
dc.subject.other	Topology	en
dc.subject.other	Approximation theory	en
dc.title	Approximate gradient projection method with Runge-Kutta schemes for optimal control problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1023/B:COAP.0000039490.61195.86	en
heal.identifier.secondary	http://dx.doi.org/10.1023/B:COAP.0000039490.61195.86	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. The state equation is discretized by the explicit fourth order Runge-Kutta scheme and the controls are approximated by discontinuous piecewise affine ones. We then propose an approximate gradient projection method that generates sequences of discrete controls and progressively refines the discretization during the iterations. Instead of using the exact discrete directional derivative, which is difficult to calculate, we use an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation by the same Runge-Kutta scheme and the integral involved by Simpson's integration rule, both involving intermediate approximations. The main result is that accumulation points, if they exist, of sequences constructed by this method satisfy the weak necessary conditions for optimality for the continuous problem. Finally, numerical examples are given.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	Computational Optimization and Applications	en
dc.identifier.doi	10.1023/B:COAP.0000039490.61195.86	en
dc.identifier.isi	ISI:000223535300005	en
dc.identifier.volume	29	en
dc.identifier.issue	1	en
dc.identifier.spage	91	en
dc.identifier.epage	115	en