@IosifPinelis the data was calculated in complete detail from ca 30k values of heart beat intervals. By the image of the PDF I mean the plot of the function and not an image in the mathematical sense.

@MarcoRipà can you please fix the picture in your question; it is no connected spanning tree and can you also clearly define whether the tree edges connect corners of the hypercube or if there may also be other vertices?

@LSpice that is the case

@LSpice Siebert is the birthname of Bodo Manthey; he is also the author of some subsequent papers that are related to the topic of calculating cycle covers with bounds on cycle lengths.

If the function isn't unimodal, the method will likely end up in a local minimum; would need some experiments to see how bad that actually gets.

sorry to object, but Brent's method makes no use of derivatives, only of the unimodularity of a function, i.e. that every local minimum is also the global minimum; correct me if I'm wrong.

One could also make an educated guess for the mean of the solution, replace every edgeweight with the squared distance from that value and the calculate the minimum weight matching with that weights; if one is bold enough he could let Brent's optimization without derivatives handle the task of finding the optimal mean.

that seems to be the only reasonable method...

Its analogous to calculating the coefficients of an approximating polynomial; there one also tries to find a set of parameters that minimizes some error measure