English

Global solutions for the sensors placement problem via weakly convex optimization

Optimization and Control 2026-07-17 v1

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\varepsilon-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\varepsilon or certifies its ε\varepsilon-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.

Cite

@article{arxiv.2607.15821,
  title  = {Global solutions for the sensors placement problem via weakly convex optimization},
  author = {Giovanni Bruccola},
  journal= {arXiv preprint arXiv:2607.15821},
  year   = {2026}
}