Abstract
In the graph partitioning problem, as in other NP-hard problems, the problem of proving the existence of a cut of given size is easy and can be accomplished by exhibiting a solution with the correct value. On the other hand proving the non-existence of a cut better than a given value is very difficult. We consider the problem of maximizing a quadratic function x T Q x where Q is an n × n real symmetric matrix with x an n-dimensional vector constrained to be an element of {−1, 1} n. We had proposed a technique for obtaining upper bounds on solutions to the problem using a continuous approach in [4]. In this paper, we extend this method by using techniques of differential geometry.
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Kamath, A., Karmarkar, N. A continuous method for computing bounds in integer quadratic optimization problems. J Glob Optim 2, 229–241 (1992). https://doi.org/10.1007/BF00171827
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DOI: https://doi.org/10.1007/BF00171827