Exploiting Sparsity for Semi-Algebraic Set Volume Computation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00357943" target="_blank" >RIV/68407700:21230/22:00357943 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10208-021-09508-w" target="_blank" >https://doi.org/10.1007/s10208-021-09508-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10208-021-09508-w" target="_blank" >10.1007/s10208-021-09508-w</a>

Result language
angličtina
Original language name
Exploiting Sparsity for Semi-Algebraic Set Volume Computation
Original language description
We provide a systematic deterministic numerical scheme to approximate the volume (i.e., the Lebesgue measure) of a basic semi-algebraic set whose description follows a correlative sparsity pattern. As in previous works (without sparsity), the underlying strategy is to consider an infinite-dimensional linear program on measures whose optimal value is the volume of the set. This is a particular instance of a generalized moment problem which in turn can be approximated as closely as desired by solving a hierarchy of semidefinite relaxations of increasing size. The novelty with respect to previous work is that by exploiting the sparsity pattern we can provide a sparse formulation for which the associated semidefinite relaxations are of much smaller size. In addition, we can decompose the sparse relaxations into completely decoupled subproblems of smaller size, and in some cases computations can be done in parallel. To the best of our knowledge, it is the first contribution that exploits correlative sparsity for volume computation of semi-algebraic sets which are possibly high-dimensional and/or non-convex and/or non-connected.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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