  We convert, within polynomial-time and sequential processing, an NP-Complete
Problem into a real-variable problem of minimizing a sum of Rational Linear
Functions constrained by an Asymptotic-Linear-Program. The coefficients and
constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the
time parameter that tends to positive infinity. The number of variables,
constraints, and rational linear functions in the objective, of the
real-variable problem is bounded by a polynomial function of the size of the
NP-Complete Problem. The NP-Complete Problem has a feasible solution,
if-and-only-if, the real-variable problem has a feasible optimal objective
equal to zero. We thus show the strong NP-hardness of this real-variable
optimization problem.
