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arXiv · 2607.15821

Global solutions for the sensors placement problem via weakly convex optimization

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

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Giovanni Bruccola. 2026-07-17. Global solutions for the sensors placement problem via weakly convex optimization. https://arxiv.org/abs/2607.15821

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