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Space Exploration: Partial Covering and Quantization

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High-Dimensional Optimization

Part of the book series: SpringerBriefs in Optimization ((BRIEFSOPTI))

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Abstract

The main developments in this chapter are:

  1. (a)

    accurate approximations for the volume of the intersection of a cube and a union of balls in \(\mathbb {R}^d\) and for the mean-square quantization error,

  2. (b)

    efficient exploration schemes for partial covering and quantization in the non-asymptotic regime,

  3. (c)

    demonstration of why the exploration schemes based on the asymptotic arguments lead to poor practical recommendations in medium and high dimensions, and

  4. (d)

    detailed theoretical study of the covering scheme based on the use of the checkerboard lattice.

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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Cardiff, UK

    Jack Noonan & Anatoly Zhigljavsky

Authors
  1. Jack Noonan
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  2. Anatoly Zhigljavsky
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Noonan, J., Zhigljavsky, A. (2024). Space Exploration: Partial Covering and Quantization. In: High-Dimensional Optimization. SpringerBriefs in Optimization. Springer, Cham. https://doi.org/10.1007/978-3-031-58909-6_2

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