LIFTING PROJECTIONS OF CONVEX POLYHEDRA,
Abstract
Briefly, if T is a projection of a closed polyhedron P onto a polyhedron Q, then a lifting of Q into P is defined to be a single-valued inverse T* of T such that T*(Q) is the union of closed faces of P. The main result of this paper, called the Lifting Theorem, asserts that there always exists a lifting T*, provided only that there exists at least one face of P on which T acts one-to-one. The Lifting Theorem is seen as a unifying generalization of a number of results in the theory of convex polyhedra and has important applications in the theory of mathematical programming. In the course of proving the Lifting Theorem a result on linear programs of interest in its own right is proven, namely, that the optimal solution of a linear program can be chosen so that it is a continuous function of the right-hand sides. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1968
- Accession Number
- AD0671427
Entities
People
- David W. Walkup
- R. J. -b. Wets
Organizations
- Boeing