On the computation of the cosine measure in high dimensions

Abstract

In derivative-free optimization, the cosine measure is a value that often arises in the convergence analysis of direct search methods. Given the increasing interest in high-dimensional derivative-free optimization problems, it is valuable to compute the cosine measure in this setting; however, it has recently been shown to be NP-hard. We propose a new formulation of the problem and heuristic to tackle this problem in higher dimensions and compare it with existing algorithms in the literature. In addition, new results are presented to facilitate the construction of sets with specific cosine measures, allowing for the creation of a test-set to benchmark the algorithms with.