Optimal control and relaxation of nonlinear elliptic systems

Papageorgiou, NS

dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:08:59Z
dc.date.available	2014-03-01T01:08:59Z
dc.date.issued	1992	en
dc.identifier.issn	0026-9255	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10773
dc.subject	Cost Function	en
dc.subject	Elliptic Partial Differential Equation	en
dc.subject	Nonlinear Elliptic System	en
dc.subject	Optimal Control	en
dc.subject	State Constraints	en
dc.subject	Transition Probability	en
dc.subject.classification	Mathematics	en
dc.subject.other	RELAXED TRAJECTORIES	en
dc.subject.other	EVOLUTION-EQUATIONS	en
dc.title	Optimal control and relaxation of nonlinear elliptic systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF01299382	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF01299382	en
heal.language	English	en
heal.publicationDate	1992	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 Λ-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. © 1992 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Monatshefte für Mathematik	en
dc.identifier.doi	10.1007/BF01299382	en
dc.identifier.isi	ISI:A1992KK67900005	en
dc.identifier.volume	114	en
dc.identifier.issue	3-4	en
dc.identifier.spage	209	en
dc.identifier.epage	244	en