Non linear constraint optimisation problem

[CollinMak]

trafficstars

I have a non-linear constraint problem as below:

The objective and constraint functions can be expressed as the sum of 4th polynomial equations like below:

where $a_i, b_i, c_i, d_i, e_i, p_i, q_i, r_i, s_i, t_i, l_i, u_i$ are some real constants.

I need to solve this type of problem multiple times daily with a high dimension $x$ (with $n$ = 200k or even 1m). I am wondering which algorithm is most suitable for this type of problem? Apologies if this is not directly relevant to the package.

[jschueller]

I think praxis or subplex are suited for high dimension, maybe others work too