Let C and K be closed cones in Rn. Denote by φ (K∩C) the face of C generated by K ∩ C, by φ(K ∩ D)D the dual face of φ(K ∩ C) in C∗, and by φ(-K∗ ∩ C∗) the face of C∗ generated by -K∗ ∩ C∗. It is proved that φ(K ∩ C∗) if and only if -C∗ ∩ [span(K ∩ C)] ⊥ ⊆ C∗ + K∗. In particular, the closedness of C∗ + K∗ is a sufficient condition. Our result contains a generalization of the Gordon-Stiemke theorem which appeared in a recent paper of Saunders and Schneider.
關聯:
Linear Algebra and Its Applications 61(C), pp.83-89
