Optimisation problem for bivariate functions

Hi, I have the following equation:

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.

Is there anything in matlab for optimisation problems or any methods I could use?

Thanks

Answer 1

[Alan Weiss]

fminsearch solves multivariable minimization problems. Also, if you have a license for it, Optimization Toolbox solves such problems more efficiently.

You might want to look at Curve Fitting Via Optimization to get some ideas how you might use fminsearch to help you.

Alan Weiss

MATLAB mathematical toolbox documentation