Optimal control and relaxation of nonlinear elliptic systems

Papageorgiou, NS

dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:08:28Z
dc.date.available	2014-03-01T01:08:28Z
dc.date.issued	1991	en
dc.identifier.issn	09167005	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10513
dc.subject	Γ-regularization	en
dc.subject	elliptic operator	en
dc.subject	necessary conditions	en
dc.subject	relaxed system	en
dc.subject	selection theorem	en
dc.subject	transition probabilities	en
dc.title	Optimal control and relaxation of nonlinear elliptic systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF03167150	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF03167150	en
heal.publicationDate	1991	en
heal.abstract	In this paper we study the optimal control of systems driven by nonlinear elliptic partial differential equations. First with the aid of an appropriate convexity hypothesis we establish the existence of optimal admissible pairs. Then we drop the convexity hypothesis and we pass to the larger relaxed system. First we consider a relaxed system based on the Gamkrelidze-Warga approach, in which the controls are transition probabilities. We show that this relaxed problem has always had a solution and the value of the problem is that of the original one. We also introduce two alternative formulations of the relaxed problem (one of them control free), which we show that they are both equivalent to the first one. Then we compare those relaxed problems, with that of Buttazzo which is based on the Γ-regularization of the ""extended"" cost functional. Finally using a powerful multiplier rule of Ioffe-Tichomirov, we derive necessary conditions for optimality in systems with inequality state constraints. © 1991 JJIAM Publishing Committee.	en
heal.journalName	Japan Journal of Industrial and Applied Mathematics	en
dc.identifier.doi	10.1007/BF03167150	en
dc.identifier.volume	8	en
dc.identifier.issue	3	en
dc.identifier.spage	525	en
dc.identifier.epage	550	en