In this paper we show that the cut does not need to go through the query point: it can be deep or shallow. The primal framework leads to a simple analysis of the potential variation, which shows that the inequality needed for convergence of the algorithm is in fact attained at the first iterate of the feasibility step.
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Received July 3, 1996 / Revised version received July 11, 1997 Published online August 18, 1998
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Goffin, JL., Vial, JP. Shallow, deep and very deep cuts in the analytic center cutting plane method. Math. Program. 84, 89–103 (1999). https://doi.org/10.1007/s10107980011a
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DOI: https://doi.org/10.1007/s10107980011a