How partial knowledge helps to solve linear programs

Abstract

We present results on how partial knowledge helps to solve linear programs. In particular, if a linear system, Ax = b and x ≥ 0, has an interior feasible point, then we show that finding a feasible point to this system can be done in O(n2.5c(A)) iterations by the layered interior-point method, and each iteration solves a least-squares problem, where n is the dimension of vector x and c(A) is the condition number of matrix A defined by Vavasis and Ye. This complexity bound is reduced by a factor n from that when this property does not exists. We also present a result for solving the problem using a little strong knowledge. © 1996 Academic Press, Inc.