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An illumination problem: optimal apex and optimal orientation for a cone of light

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  • Annabella Astorino
  • Manlio Gaudioso
  • Alberto Seeger

Abstract

Let $$\{a_i:i\in I\}$$ be a finite set in $$\mathbb R ^n$$ . The illumination problem addressed in this work is about selecting an apex $$z$$ in a prescribed set $$Z\subseteq \mathbb R ^n$$ and a unit vector $$y\in \mathbb R ^n$$ so that the conic light beam $$\begin{aligned} C(z,y,s):= \{x \in \mathbb R ^n : s\,\Vert x-z\Vert - \langle y, x-z\rangle \le 0\} \end{aligned}$$ captures every $$a_i$$ and, at the same time, it has a sharpness coefficient $$ s\in [0,1]$$ as large as possible. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Annabella Astorino & Manlio Gaudioso & Alberto Seeger, 2014. "An illumination problem: optimal apex and optimal orientation for a cone of light," Journal of Global Optimization, Springer, vol. 58(4), pages 729-750, April.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:4:p:729-750
    DOI: 10.1007/s10898-013-0071-0
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    References listed on IDEAS

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    1. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
    2. Annabella Astorino & Antonio Fuduli & Manlio Gaudioso, 2012. "Margin maximization in spherical separation," Computational Optimization and Applications, Springer, vol. 53(2), pages 301-322, October.
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    Cited by:

    1. Alberto Seeger & José Vidal -Nuñez, 2017. "Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach," Journal of Global Optimization, Springer, vol. 68(2), pages 279-306, June.

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