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An enhanced logical benders approach for linear programs with complementarity constraints. (English) Zbl 1447.90040
Summary: This work extends the logical Benders approach for solving linear programs with complementarity constraints proposed by J. Hu et al. [SIAM J. Optim. 19, No. 1, 445–471 (2008; Zbl 1163.90031)] and L. Bai et al. [Comput. Optim. Appl. 54, No. 3, 517–554 (2013; Zbl 1295.90035)]. We develop a novel interpretation of the logical Benders method as a reversed branch-and-bound search, where the whole exploration procedure starts from the leaf nodes in an enumeration tree. This insight enables us to provide a new framework over which we can combine the master problem and the cut generation in a single process. It also allows us to diversify the search, leading computationally to stronger cuts. We also present an optimization-based sparsification process which makes the cut generation more efficient. Numerical results are presented to show the effectiveness of this enhanced method. Results are also extended to problems with more complementarity constraints, exceeding those that can be handled by the original method in the cited references.
##### MSC:
 90C26 Nonconvex programming, global optimization 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
##### Software:
CPLEX; Gurobi; LPCCbnc; MacMPEC
Full Text:
##### References:
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