Displaying similar documents to “Optimisation in space of measures and optimal design”

Optimisation in space of measures and optimal design

Ilya Molchanov, Sergei Zuyev (2010)

ESAIM: Probability and Statistics

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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...

Vector variational problems and applications to optimal design

Pablo Pedregal (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...

D-optimal and highly D-efficient designs with non-negatively correlated observations

Krystyna Katulska, Łukasz Smaga (2016)

Kybernetika

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In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be...

Vector variational problems and applications to optimal design

Pablo Pedregal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...

On an optimal shape design problem in conduction

José Carlos Bellido (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.