Accession Number : AD0671427

Title :   LIFTING PROJECTIONS OF CONVEX POLYHEDRA,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Walkup,David W. ; Wets,R. J. -B.

Report Date : APR 1968

Pagination or Media Count : 20

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)

Descriptors :   (*MATHEMATICAL PROGRAMMING, THEOREMS), (*TRANSFORMATIONS(MATHEMATICS), PROJECTIVE GEOMETRY), LINEAR PROGRAMMING, OPTIMIZATION, PROBLEM SOLVING, SET THEORY, PERTURBATION THEORY

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE