Hyperplane Arrangements in Optimization

Abstract

A face f is called a k-face if its dimension is k. Special names are used to denote k-faces for special values of k: a 0-face is called a vertex, a 1-face is called an edge, a (d–1)-face is called a facet, and a d-face is called a cell. A face is said to be a subface of another face g if the dimension of f is one less than the dimension of g and f is contained in the boundary of g; it follows that si (f)= 0 unless si (f)= si (g) for 1≤ i≤ n.