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Currently, I am reading the paper "Exploring relaxation induced neighborhood to improve MIP solutions" by Danna et.al. from 2004 and they are talking about a symmetric role of incumbent and the relaxed solution. Which I understood as following:

An incumbent of poor quality can be improved because the respective relaxation is leading into a good direction. And vice versa, a loose relaxation can be compensated by an incumbent of good quality.

How does it work? Can it not happen that it still continues into a completely bad direction?

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    $\begingroup$ Welcome to CS.SE! Do you by any chance have a link to a freely available PDF of the paper? $\endgroup$ – D.W. Feb 29 '16 at 19:23
  • $\begingroup$ Can you see the full text here: download.springer.com/static/pdf/696/…*~hmac=7b18027492f15466ea8d93356d3c7d034b635e29959bee1871bb302bef8d96ab ? $\endgroup$ – steph Feb 29 '16 at 19:30

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