Existence and Relaxation for Finite-Dimensional Optimal Control Problems Driven by Maximal Monotone Operators

Papageorgiou, NS; Papalini, F

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Papalini, F	en
dc.date.accessioned	2014-03-01T01:18:58Z
dc.date.available	2014-03-01T01:18:58Z
dc.date.issued	2003	en
dc.identifier.issn	0232-2064	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15294
dc.subject	Γ-regularization	en
dc.subject	Admissible relaxation	en
dc.subject	Carathéodory's theorem	en
dc.subject	Maximal monotone operator	en
dc.subject	Multi-valued dynamics	en
dc.subject	Multiple Γ-limits	en
dc.subject	Reduction method	en
dc.subject	Relaxed problem	en
dc.subject	Variational inequalities	en
dc.subject	Young measure	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	UNILATERAL CONSTRAINTS	en
dc.subject.other	INTEGRAL FUNCTIONALS	en
dc.subject.other	LOWER SEMICONTINUITY	en
dc.subject.other	LAGRANGE PROBLEMS	en
dc.subject.other	THEOREMS	en
dc.subject.other	WEAK	en
dc.title	Existence and Relaxation for Finite-Dimensional Optimal Control Problems Driven by Maximal Monotone Operators	en
heal.type	journalArticle	en
heal.identifier.primary	10.4171/ZAA/1177	en
heal.identifier.secondary	http://dx.doi.org/10.4171/ZAA/1177	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	In this paper we study the optimal control of a class of nonlinear finite-dimensional optimal control problems driven by a maximal monotone operator which is not necessarily everywhere defined. So our model problem incorporates systems monitored by variational inequalities. First we prove an existence theorem using the reduction method of Berkovitz and Cesari. This requires a convexity hypothesis. When this convexity condition is not satisfied, we have to pass to an augmented, convexified problem known as the "relaxed problem". We present four relaxation methods. The first uses Young measures, the second uses multi-valued dynamics, the third is based on Caratheodory's theorem for convex sets in R-N and the fourth uses lower semicontinuity arguments and Gamma-limits. We show that they are equivalent and admissible, which roughly speaking means that the corresponding relaxed problem is in a sense the "closure" of the original one.	en
heal.publisher	HELDERMANN VERLAG	en
heal.journalName	Zeitschrift fur Analysis und ihre Anwendung	en
dc.identifier.doi	10.4171/ZAA/1177	en
dc.identifier.isi	ISI:000220459900008	en
dc.identifier.volume	22	en
dc.identifier.issue	4	en
dc.identifier.spage	863	en
dc.identifier.epage	898	en