Unconstrained Binary Quadratic Programming
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Given a collection of :math:`n` items such that each pair of items is associated with a profit value that can be positive, negative or zero, unconstrained binary quadratic programming (UBQP) seeks a subset of items that maximizes the sum of their paired values. The value of a pair is accumulated in the sum only if the two corresponding items are selected.

The UBQP problem will be tackle in this example.

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   :caption: Contents:

   problem
   instance
   implementation