# Optimisation in space of measures and optimal design

ESAIM: Probability and Statistics (2010)

- Volume: 8, page 12-24
- ISSN: 1292-8100

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topMolchanov, Ilya, and Zuyev, Sergei. "Optimisation in space of measures and optimal design." ESAIM: Probability and Statistics 8 (2010): 12-24. <http://eudml.org/doc/104314>.

@article{Molchanov2010,

abstract = {
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.
},

author = {Molchanov, Ilya, Zuyev, Sergei},

journal = {ESAIM: Probability and Statistics},

keywords = {Optimal experimental design; generalized equivalence theorem; constrained optimal design; Poisson design; optimization on measures; gradient methods.; gradient methods},

language = {eng},

month = {3},

pages = {12-24},

publisher = {EDP Sciences},

title = {Optimisation in space of measures and optimal design},

url = {http://eudml.org/doc/104314},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Molchanov, Ilya

AU - Zuyev, Sergei

TI - Optimisation in space of measures and optimal design

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 12

EP - 24

AB -
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.

LA - eng

KW - Optimal experimental design; generalized equivalence theorem; constrained optimal design; Poisson design; optimization on measures; gradient methods.; gradient methods

UR - http://eudml.org/doc/104314

ER -

## References

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