A method of transferring polyhedron between the intersection-form and the sum-form

✍ Scribed by Quanling Wei; Hong Yan

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 781 KB
• Volume: 41
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(01)00100-6

✦ Synopsis

bounded polyhedron (or a polyhedral cone) can be given by either an intersection of linear inequalities, which is thus called intersection-form, or a convex combination (or nonnegative linear combination) of some given points, which is thus called sum-form. This paper first proposes a simple and effective method to transfer a bounded polyhedron or a polyhedral cone from the intersection-form to the sum-form. A new method is proposed to transfer a bounded polyhedron (or a polyhedral cone) from the sum-form to the intersection form. Both procedures can be completed in finite number of iterations. Numerical examples are given for illustration.