Bilinear Separation of Two Sets in n-Space (1993)
| Venue: | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS |
| Citations: | 32 - 17 self |
BibTeX
@ARTICLE{Bennett93bilinearseparation,
author = {Kristin P. Bennett and O. L. Mangasarian},
title = {Bilinear Separation of Two Sets in n-Space},
journal = {COMPUTATIONAL OPTIMIZATION AND APPLICATIONS},
year = {1993},
volume = {2}
}
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Abstract
The NP-complete problem of determining whether two disjoint point sets in the n-dimensional real space R n can be separated by two planes is cast as a bilinear program, that is minimizing the scalar product of two linear functions on a polyhedral set. The bilinear program, which has a vertex solution, is processed by an iterative linear programming algorithm that terminates in a finite number of steps at a point satisfying a necessary optimality condition or at a global minimum. Encouraging computational experience on a number of test problems is reported.
