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Here's the answer I found out: The analytical equations can be solved as a convex optimization problem. i.e by keeping all terms on one side and introducing an inequality constraint. For example, in this problem, dP/drho = (dRp/drho)*Rp' + Rp*(dRp/drho)' can be written as ((dRp/drho)*Rp' + Rp*(dRp/drho)' -dP/drho) >=0 and then solve an optimiation ...

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