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A lexicographic algebraic theorem and its applications

✍ Scribed by Satoru Fujishige; Zaifu Yang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 968 KB
Volume: 279
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)00002-0

No coin nor oath required. For personal study only.

✦ Synopsis

In this Paper we prove the following result: Given any full-dimensional simple polytope P = {x E R" 1 a'=.x < bi, i = 1,. . , WZ} without redundant constraints and any vector c E iw", there exists a unique vertex x* of P such that the matrix

exists and is lexicographic positive, where x* is the Solution of the n linear equations a'rrX = b. r = 1 . II T , "> n. This theorem generalizes a result on the n-dimensional cube and tan be used to resolve the degeneracy Problem for simplicial fixed Point algorithms. We also discuss several applications for this result.

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