MENÜ MENÜ  

cover

Black box optimization with exact subsolvers. A radial basis function algorithm for problems with convex constraints

Christine Edman

ISBN 978-3-8325-4329-7
122 pages, year of publication: 2016
price: 38.50 €
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.

cover cover cover cover cover cover cover cover cover
Table of contents (PDF)

Keywords:

  • Black box optimization
  • Global optimization
  • RBF-method
  • Convex constraints
  • Conditional positive definite

Buying Options

38.50 €

36.50 €
48.50 €
52.50 €

(D) = Within Germany
(W) = Abroad

*You can purchase the eBook (PDF) alone or combined with the printed book (eBundle). In both cases we use the payment service of PayPal for charging you - nevertheless it is not necessary to have a PayPal-account. With purchasing the eBook or eBundle you accept our licence for eBooks.

For multi-user or campus licences (MyLibrary) please fill in the form or write an email to order@logos-verlag.de