Technique/solver to handle a constraint of degree 5

[Khalil Ben Safta]

Hello,

I am working on an optimization that involves an equality constraint with an unknown raised to the power 5.

Where π and d are my (positive real) unknowns/decision variables. All other values are known.

The specific question would be: what (ideally free for academic use) solver could handle this constraint ?

Or, if no solver is able to do it, what preprocessing technique could be used to make this constraint "handleable" by a solver? I saw for example that Gurobi is able to handle piecewise linear constraints. Could the (above written) constraint be linearized ? This would be ideal since I am using pyomo (Python-based algebraic modelling language) and I have Gurobi correctly working with it. I am also trying to install Ipopt, however unsuccessfully till now.

For those interested on the background, this equation represents actually the pressure drop in a pipeline. The problem is about optimally sizing the diameters of a network of gas pipelines. the objective function is

Where l_ij is the length of the pipelines and a_0,a_1 and a_2 are coefficients.

Thanks.