Analytic centers and repelling inequalities

ct 9 The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling 10 path is a generalization of the analytic central path for linear programming, and we show that this path has a unique 11 limit. Furthermore, this limit is the prime analytic center if the set of repelling inequalities contains only those con12 straints that ``shape'' the polytope. Because we allow lower dimensional polytopes, the proof techniques are non13 standard and follow from data perturbation analysis. This analysis overcomes the difficulty that analytic centers of 14 lower dimensional polytopes are not necessarily continuous with respect to the polytope's data representation. A second 15 concept introduced here is that of the ``prime analytic center'', in which we establish its uniqueness in the absence of 16 redundant inequalities. Again, this is well known for full dimensional polytopes, but it is not immediate for lower 17 dimens...

• Type: Journal
• Year: 2002
• Where: EOR
• Authors: Richard J. Caron, Harvey J. Greenberg, Allen G. Holder
• Keywords: Dimensional Polytopes, EOR 2002, Prime Analytic Center, Repelling