Discretization methods for nonconvex optimal control problems with state constraints

Chryssoverghi, I; Coletsos, I; Kokkinis, B

dc.contributor.author	Chryssoverghi, I	en
dc.contributor.author	Coletsos, I	en
dc.contributor.author	Kokkinis, B	en
dc.date.accessioned	2014-03-01T01:22:12Z
dc.date.available	2014-03-01T01:22:12Z
dc.date.issued	2005	en
dc.identifier.issn	0163-0563	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16485
dc.subject	Discrete penalized conditional descent method	en
dc.subject	Discretization	en
dc.subject	Midpoint scheme	en
dc.subject	Optimal control	en
dc.subject	Relaxed controls	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation theory	en
dc.subject.other	Constraint theory	en
dc.subject.other	Differential equations	en
dc.subject.other	Functions	en
dc.subject.other	Problem solving	en
dc.subject.other	Theorem proving	en
dc.subject.other	Discrete penalized conditional descent method	en
dc.subject.other	Discretization	en
dc.subject.other	Midpoint scheme	en
dc.subject.other	Optimal control	en
dc.subject.other	Relaxed controls	en
dc.subject.other	Optimal control systems	en
dc.title	Discretization methods for nonconvex optimal control problems with state constraints	en
heal.type	journalArticle	en
heal.identifier.primary	10.1081/NFA-200067296	en
heal.identifier.secondary	http://dx.doi.org/10.1081/NFA-200067296	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We consider an optimal control problem described by nonlinear ordinary differential equations, with control and state constraints, including pointwise state constraints. Because no convexity assumptions are made, the problem may have no classical solutions, and it is reformulated in relaxed form. The relaxed control problem is then discretized by using the implicit midpoint scheme, while the controls are approximated by piecewise constant relaxed controls. We first study the behavior in the limit of properties of discrete relaxed optimalily, and of discrete relaxed admissibility and extremality. We then apply a penalized conditional descent method to each discrete relaxed problem, and also a corresponding discrete method to the continuous relaxed problem that progressively refines the discretization during the iterations, thus reducing computing time and memory. We prove that accumulation points of sequences generated by these methods are admissible and extremal for the discrete or the continuous problem. Finally, numerical examples are given. Copyright © Taylor & Francis, Inc.	en
heal.publisher	TAYLOR & FRANCIS INC	en
heal.journalName	Numerical Functional Analysis and Optimization	en
dc.identifier.doi	10.1081/NFA-200067296	en
dc.identifier.isi	ISI:000230890800003	en
dc.identifier.volume	26	en
dc.identifier.issue	3	en
dc.identifier.spage	321	en
dc.identifier.epage	348	en