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Is it not easy to "trick" Dr. Ampl into
believing a convex expression is nonconvex?
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While it is true that the two expressions
(x - 1)4 and
x4 - 4 x3 + 6 x2 - 4 x + 1
are equivalent and convex everywhere, Dr. Ampl will believe
that for x > 0, the second one is nonconvex because of
the term -4 x3. However, Dr. Ampl was not
designed to be a symbolic computation platform and should never
be expected to realize that the two above expressions are equal.
We believe that it is the responsibility of the modeler to use
the appropriate expression in their model not to make the
problem unnecessarily complex.
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