Optimisation in space of measures and optimal design

Molchanov, Ilya; Zuyev, Sergei (2004). Optimisation in space of measures and optimal design. ESAIM: Probability and Statistics, 8, pp. 12-24. EDP Sciences 10.1051/ps:2003016

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The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework makes it possible to use the whole arsenal of descent algorithms from the general optimisation literature for finding optimal designs. The corresponding steepest descent involves adding a signed measure at every step and converges faster than the conventional sequential algorithms used to construct optimal designs. We study a new class of design problems when the observation points are distributed according to a Poisson point process arising in the situation when the total control on the placement of measurements is impossible.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

1292-8100

Publisher:

EDP Sciences

Language:

English

Submitter:

Ilya Molchanov

Date Deposited:

09 Aug 2016 07:33

Last Modified:

09 Aug 2016 07:33

Publisher DOI:

10.1051/ps:2003016

BORIS DOI:

10.7892/boris.85368

URI:

https://boris.unibe.ch/id/eprint/85368

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