A lexicographic algebraic theorem and its applications Original Research Article

In this paper we prove the following result: Given any full-dimensional simple polytope P = {x set membership, variant imagen ¦ aiTx ≤ bi, I = 1, …, m} without redundant constraints and any vector c set membership, variant imagen, there exists a unique vertex x* of P such that the matrix image exists and is lexicographic positive, where x* is the solution of the n linear equations aitT X = bit, t = 1, …, n. This theorem generalizes a result on the n-dimensional cube and can be used to resolve the degeneracy problem for simplicial fixed point algorithms. We also discuss several applications for