Hans Becker, Frank Schmidt, et al.
Photomask and Next-Generation Lithography Mask Technology 2004
In recent years there has been growing interest in generating valid inequalities for mixed-integer programs using sets with two or more constraints. In particular, Andersen et al. (2007) [2] and Borozan and Cornujols (2009) [3] have studied sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach have already been computationally studied by Espinoza (2008) [8] for general mixed-integer problems, and there is ongoing computational research in this area. In this paper, we extend the model studied in the earlier papers and require the integer variables to be non-negative. We extend the results in [2] and [3] to our case, and show that cuts generated by their approach can be strengthened by using the non-negativity of the integer variables. In particular, it is possible to obtain cuts which have negative coefficients for some variables. © 2010 Elsevier B.V. All rights reserved.
Hans Becker, Frank Schmidt, et al.
Photomask and Next-Generation Lithography Mask Technology 2004
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Fausto Bernardini, Holly Rushmeier
Proceedings of SPIE - The International Society for Optical Engineering
Satoshi Hada
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences