LEADER 02903nam 2200409 450 001 9910816159303321 005 20230626121434.0 010 $a3-8325-9146-X 035 $a(CKB)4910000000017349 035 $a(MiAaPQ)EBC5850400 035 $a5a8e86f4-3ba8-4dc9-8206-66c5b0dd2d03 035 $a(EXLCZ)994910000000017349 100 $a20190909d2016 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBlack box optimization with exact subsolvers $ea radial basis function algorithm for problems with convex constraints /$fvorgelegt von Christine Edman 210 1$aTrier :$cLogos Verlag Berlin GmbH,$d[2016] 210 4$dİ2016 215 $a1 online resource (iv, 114 pages) $cillustrations 300 $a"Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) ... Dem Fachberich IV der Universita?t Trier, Trier, 2016." 311 $a3-8325-4329-5 320 $aIncludes bibliographical references (111-114). 330 $aLong description: We consider expensive optimization problems, that is to say problems where each evaluation of the objective function is expensive in terms of computing time, consumption of resources, or cost. This often happens in situations where the objective function is not available in analytic form, e.g. crash tests, best composition of chemicals, or soil contamination. Due to this lack of analytical representation we also speak about `black box functions'. In order to use as few function evaluations as possible within the optimization process, a sophisticated strategy to determine the evaluation points is necessary. In this thesis we present an algorithm which belongs to the class of the wellknown Radial basis function (RBF)-methods. RBF-methods usually incorporate subproblems which are difficult to solve exact. In order to solve these problems exact, we developed a Branch & Bound routine. This routine computes lower bounds by using the property of `conditional positive definiteness' of the RBF. We present a formula for the inverse of a blockmatrix with solely singular diagonal blocks. We also present a partitioning rule for multidimensional rectangles, which gives much freedom in the choice of the bisection point subject to preserve the important property of `exhaustiveness'. We tested our algorithm and present results for both expensive problems with only box constraints and expensive problems with general convex constraints. 606 $aRadial basis functions 615 0$aRadial basis functions. 676 $a511.42 700 $aEdman$b Christine$01676087 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816159303321 996 $aBlack box optimization with exact subsolvers$94042040 997 $aUNINA