A simpler and tighter redundant Klee-Minty construction

By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the edges of the Klee-Minty cubes, thus having 2n - 2 sharp turns in dimension n. In those constructions the redundant hyperplanes were placed parallel with the facets active at the optimal solution. In this paper we present a simpler and more powerful construction, where the redundant constraints are parallel with the coordinate-planes. An important consequence of this new construction is that one of the sets of redundant hyperplanes is touching the feasible region, and N, the total number of the redundant hyperplanes is reduced by a factor of n2 , further tightening the gap between iteration-complexity upper and lower bounds. Key words: Linear programming, Klee-Minty example, interior point methods, worst-case iteration complexity, central path.

• Type: Journal
• Year: 2008
• Where: OL
• Authors: Eissa Nematollahi, Tamás Terlaky
• Keywords: Klee-minty Example, OL 2008, Redundant Hyperplanes, Redundant Klee-minty Examples