Pareto robust optimization on Euclidean vector spaces

Pareto Efficiency in Robust Optimization

This paper formalizes and adapts the well known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and illustrate via examples how this could lead to inefficiencies and sub-optimal performance in practice. We provide a basic ...

Phone classification in pseudo-euclidean vector spaces

Recently we have proposed a structural framework for modelling speech, which is based on patterns of phonological distinctive features, a linguistically well-motivated alternative to standard vector-space acoustic models like HMMs. This framework gives considerable representational freedom by working with features that have explicit linguistic interpretation, but at the expense of the ability t...

On $beta-$topological vector spaces

We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.  

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

On Isometries of Euclidean Spaces