65K05 Mathematical programming methods [See also 90Cxx]
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- 2011 (1)
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- linear programming bounds (1) (remove)
Institute
Fast computation of valid linear programming (LP) bounds serves as an
important subroutine for solving mixed-integer programming problems
exactly. We introduce a new method for computing valid LP bounds designed
for this application. The algorithm corrects approximate LP dual solutions
to be exactly feasible, giving a valid bound. Solutions are repaired by
performing a projection and a shift to ensure all constraints are
satisfied; bound computations are accelerated by reusing structural
information through the branch-and-bound tree. We demonstrate this method
to be widely applicable and faster than solving a sequence of exact LPs.
Several variations of the algorithm are described and computationally
evaluated in an exact branch-and-bound algorithm within the mixed-integer
programming framework SCIP.