Polyhedral Sets Having a Least Element.
Abstract
For a fixed m x n matrix A, the authors consider the family of polyhedral sets X(sub b) = (x : Ax > or = b), b belongs to R(sup m), and prove a theorem characterizing in terms of A, the circumstances under which every nonempty X sub b has a least element. In the special case where A contains all the rows of an n x n identity matrix, the conditions are equivalent to A sup T being Leontief. Among the corollaries of the theorem, the authors show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 20, 1971
- Accession Number
- AD0737647
Entities
People
- Arthur F. Veinott Jr.
- Richard Cottle
Organizations
- Stanford University