Hi, I have the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

f(z)=g(z)+b*u(z)

where z=(x,y) i.e. bivariate,b is a parameter, u(z) the uniform distribution and g(z) a function that represents distance.

By considering for a momment b=0, min(f(z)) can give me the location of the minimum distance. However because I want to have locations that are not the same I add u(z). With b it's possible to change the influence of u(z). Very high values of b give very random positions, while if b is very small, only locations around the minimum are chosen.

Furthermore, I have some reference locations zr={(x1,y1),(x2,x2),...(xn,yn)}. I'm trying to figure out the best b I could have in order to produce from f(z) locations as much close as possible to zr.

Do you have any ideas of optimisation method I could use or even if I could find an analytical solution?

Thanks

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# Optimization methods with bivariate functions

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