  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.
