Descent-penalty methods for relaxed nonlinear elliptic optimal control problems

Chryssoverghi, I; Geiser, J

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Geiser, J	en
dc.date.accessioned	2014-03-01T02:51:35Z
dc.date.available	2014-03-01T02:51:35Z
dc.date.issued	2008	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35576
dc.subject.other	Accumulation points	en
dc.subject.other	Classical methods	en
dc.subject.other	Classical solutions	en
dc.subject.other	Computing time	en
dc.subject.other	Control constraint	en
dc.subject.other	Control variable	en
dc.subject.other	Cost functionals	en
dc.subject.other	Discrete Control	en
dc.subject.other	Discretizations	en
dc.subject.other	Extremal	en
dc.subject.other	Galerkin finite element methods	en
dc.subject.other	Non-Linearity	en
dc.subject.other	Numerical example	en
dc.subject.other	Optimal control problem	en
dc.subject.other	Optimization method	en
dc.subject.other	Penalty methods	en
dc.subject.other	Relaxed problem	en
dc.subject.other	Second order elliptic	en
dc.subject.other	State constraints	en
dc.subject.other	Computational fluid dynamics	en
dc.subject.other	Computer science	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Refining	en
dc.subject.other	Optimization	en
dc.title	Descent-penalty methods for relaxed nonlinear elliptic optimal control problems	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-540-78827-0_33	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-540-78827-0_33	en
heal.publicationDate	2008	en
heal.abstract	An optimal control problem is considered, described by a second order elliptic partial differential equation, jointly nonlinear in the state and control variables, with high monotone nonlinearity in the state, and with control and state constraints. Since no convexity assumptions are made, the problem may have no classical solutions, and so it is reformulated in the relaxed form. The relaxed problem is discretized by a Galerkin finite element method for state approximation, while the controls are approximated by elementwise constant relaxed ones. The first result is that relaxed accumulation points of sequences of admissible and extremal discrete controls are admissible and extremal for the continuous relaxed problem. We then propose a mixed conditional descent-penalty method, applied to a fixed discrete relaxed problem, and also a progressively refining version of this method that reduces computing time and memory. We show that accumulation points of sequences generated by the fixed discretization (resp. progressively refining) method are admissible and extremal for the discrete (resp. continuous) relaxed problem. Numerical examples are given. This paper proposes relaxed discretization and optimization methods instead of the corresponding classical methods presented in [5]. Considered here problems are with not necessarily convex control constraint sets, and with state constraints and cost functionals depending also on the state gradient. Also, the results of Sections 1 and 2 generalize those of [8] w.r.t. the assumptions made. © 2008 Springer.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-540-78827-0_33	en
dc.identifier.volume	4818 LNCS	en
dc.identifier.spage	300	en
dc.identifier.epage	308	en