Global optimality conditions for sensor placement, with extensions to binary low-rank A-optimal designs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909842690539520 |
|---|---|
| author | Aarset, Christian |
| author_facet | Aarset, Christian |
| contents | The \emph{sensor placement problem} for stochastic linear inverse problems consists of determining the optimal manner in which sensors can be employed to collect data. Specifically, one wishes to place a limited number of sensors over a large number of candidate locations, quantifying and optimising over the effect this data collection strategy has on the solution of the inverse problem. In this article, we provide a global optimality condition for the sensor placement problem via a subgradient argument, obtaining sufficient and necessary conditions for optimality\revix{, and marking certain sensors as \emph{dominant} or \emph{redundant}, i.e.~always on or always off}. We demonstrate how to take advantage of this optimality criterion to find approximately optimal binary designs, i.e.~designs where no fractions of sensors are placed. Leveraging our optimality criteria, we derive a powerful low-rank formulation of the A-optimal design objective for finite element-discretised function space settings, demonstrating its high computational efficiency, particularly in terms of derivatives, and study globally optimal designs for a Helmholtz-type source problem and extensions towards optimal binary designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global optimality conditions for sensor placement, with extensions to binary low-rank A-optimal designs Aarset, Christian Optimization and Control 62K05, 62F15, 35R30, 65K10, 90C25, 90C26 The \emph{sensor placement problem} for stochastic linear inverse problems consists of determining the optimal manner in which sensors can be employed to collect data. Specifically, one wishes to place a limited number of sensors over a large number of candidate locations, quantifying and optimising over the effect this data collection strategy has on the solution of the inverse problem. In this article, we provide a global optimality condition for the sensor placement problem via a subgradient argument, obtaining sufficient and necessary conditions for optimality\revix{, and marking certain sensors as \emph{dominant} or \emph{redundant}, i.e.~always on or always off}. We demonstrate how to take advantage of this optimality criterion to find approximately optimal binary designs, i.e.~designs where no fractions of sensors are placed. Leveraging our optimality criteria, we derive a powerful low-rank formulation of the A-optimal design objective for finite element-discretised function space settings, demonstrating its high computational efficiency, particularly in terms of derivatives, and study globally optimal designs for a Helmholtz-type source problem and extensions towards optimal binary designs. |
| title | Global optimality conditions for sensor placement, with extensions to binary low-rank A-optimal designs |
| topic | Optimization and Control 62K05, 62F15, 35R30, 65K10, 90C25, 90C26 |
| url | https://arxiv.org/abs/2410.16590 |