FACE

Face - A convex subset, say S, of a convex set , say C, such that [x, y] in C and [x, y] /\ ri(S) not empty imply x, y are in S. C, itself, is a face of C, and most authors consider the empty set a face. The faces of zero dimension are the extreme points of C. When C is a polyhedron , (x: Ax <= b), the faces are the subsystems with some inequalities holding with equality: (x: Bx = c, Dx <= d), where A = [B D] and b = [c' d']'.