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Abstract
We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear programming to deal with complementarity conditions. We develop an anticycling scheme that can verify Bouligand stationarity. We also give an optimization-based technique to find an initial feasible vertex. Starting with a feasible vertex, our algorithm always finds a minimizer or an unbounded descent search direction in a finite number of pivoting steps.
Acknowledgements
This work was supported by the Office of Advanced Scientific Computing Research, Office of Science, US Department of Energy, under Contract DE-AC02-06CH11357. This work was also supported by NSF grant 0631622. The submitted manuscript has been created by the UChicago Argonne, LLC, Operator of Argonne National Laboratory (‘Argonne’) under Contract No.\ DE-AC02-06CH11357 with the US Department of Energy. The US Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.