On random embeddings and their application to optimisation

Zhen Shao

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arXiv · 2206.03371

On random embeddings and their application to optimisation

Zhen Shao

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Abstract

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of optimisation, one needs to explore high-dimensional spaces representing the problem data or its parameters and thus the computational cost of solving an optimisation problem is connected to the size of the data/variables. This thesis studies the theoretical properties of norm-preserving random embeddings, and their application to several classes of optimisation problems.

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Zhen Shao. 2022-06-07. On random embeddings and their application to optimisation. https://arxiv.org/abs/2206.03371

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