A simpler and tighter redundant Klee–Minty construction
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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 2 n −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 n 2, further tightening the gap between iteration-complexity upper and lower bounds.
KeywordsLinear programming Klee–Minty example Interior point methods Worst-case iteration complexity Central path
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