# Accession Number:

## AD0671427

# Title:

## LIFTING PROJECTIONS OF CONVEX POLYHEDRA,

# Descriptive Note:

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

# Personal Author(s):

# Report Date:

## 1968-04-01

# Pagination or Media Count:

## 20.0

# 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 TQ 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

# Descriptors:

# Subject Categories:

- Operations Research