| Tartalmi leírás: |
We examine the connections between the classes of cuts in the title. We show
that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized
intersection cuts (GICs) from the family of polyhedra obtained by taking positive com-
binations of the complements of the inequalities of each term of the disjunction. While
L&P cuts from split disjunctions are known to be equivalent to standard intersection
cuts (SICs) from the strip obtained by complementing the terms of the split, we show
that L&P cuts from more general disjunctions may not be equivalent to any SIC. In
particular, we give easily verifiable necessary and sufficient conditions for a L&P cut
from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart
of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting
properties. For instance, unlike the regular ones, they may cut off part of the corner
polyhedron associated with the LP solution from which they are derived. Furthermore,
they are not exceptional: their frequency exceeds that of regular cuts. A numerical
example illustrates some of the above properties.
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