PreprintCC BY 4.0arXiv
Global solutions for the sensors placement problem via weakly convex optimization
Abstract
We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute ε-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance ε or certifies its ε-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.
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BibTeX
@misc{bruccola2026global,
title = {{Global solutions for the sensors placement problem via weakly convex optimization}},
author = {Giovanni Bruccola},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15821},
eprint = {2607.15821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15821},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global solutions for the sensors placement problem via weakly convex optimization
AU - Giovanni Bruccola
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2607.15821
UR - https://arxiv.org/abs/2607.15821
AB - We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute ε-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance ε or certifies its ε-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.
ER -