On random embeddings and their application to optimisation
Z Shao - arXiv preprint arXiv:2206.03371, 2022 - arxiv.org
arXiv preprint arXiv:2206.03371, 2022•arxiv.org
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 …
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 …
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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