论文标题
在随机嵌入及其在优化中的应用
On random embeddings and their application to optimisation
论文作者
论文摘要
随机嵌入式项目高维空间至低维空间；它们是仔细的结构，可以近似保留关键特性，例如点之间的成对距离。通常在优化领域，需要探索代表问题数据或其参数的高维空间，因此解决优化问题的计算成本与数据/变量的大小相关。本文研究了保留规范的随机嵌入的理论特性，以及它们在几类优化问题上的应用。
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.
