dc.contributor.author Neittaanmäki, Pekka dc.contributor.author Stachurski, Andrzej dc.date.accessioned 2019-03-12T11:52:59Z dc.date.available 2019-03-12T11:52:59Z dc.date.issued 1992 fi dc.identifier.citation Neittaanmäki, P., Stachurski, A. (1992). Solving some optimal control problems using the Barrier penalty function method. Applied Mathematics and Optimization 25 (2), 127-149. doi:10.1007/BF01182477 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/63104 dc.description.abstract In this paper we present a new approach to solve a two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary-value problems. The problem considered is to find a minimum of a functional with respect to the control variablesu. The minimized functional depends on control variables and state variablesx. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend onu. fi Our main idea is to replace this QP problem by its dual and then apply the barrier penalty method to this dual QP problem or to the primal one if it is in an appropriate form. As a result we obtain a problem approximating the original one. Its good property is the differentiable dependence of state variables with respect to the control variables. Furthermore, we propose a method for finding an approximate solution of a penalized lower-level problem if the optimal solution of the original QP problem is known. We apply the result obtained to some optimal shape design problems governed by the Dirichlet-Signorini boundary-value problem. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Springer dc.relation.ispartofseries Applied Mathematics and Optimization dc.rights In Copyright dc.title Solving some optimal control problems using the Barrier penalty function method fi dc.type article dc.identifier.urn URN:NBN:fi:jyu-201903121823 dc.contributor.laitos fi dc.contributor.laitos Department of Mathematics en dc.contributor.oppiaine dc.type.uri http://purl.org/eprint/type/JournalArticle dc.description.version eprint.status dc.description.reviewstatus peerReviewed dc.format.pagerange 127-149 dc.relation.issn 0095-4616 dc.relation.numberinseries 2 dc.relation.volume 25 dc.type.version publishedVersion dc.rights.copyright © Springer dc.rights.accesslevel restrictedAccess fi dc.format.content fulltext dc.rights.url http://rightsstatements.org/page/InC/1.0/?language=en dc.relation.doi 10.1007/BF01182477
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