MATLAB: Find params that minimize function

MATLABminimize

I have the function

where I know the

and σ

How can I find the two params x and y that minimize the function which variable is ξ ?

Best Answer

You can define it as an annonymous function and then call fminsearch to solve it:

e = 5;
xi = [1,2,3,4];
yi = [3,4,5,6];
sigma = 2
fun = @(x,e,xi,yi,sigma) abs(4*e- sum(sqrt( (x(1)-xi).^2-(x(2)-yi).^2  ))/(2*sigma^2));
x0 = [1,1];
[x,fval] = fminsearch(@(x)fun(x,e,xi,yi,sigma),x0)

I changed your function with an abs() function, which I believe it was your intention, otherwise your function has no minimum since it can go to -inf.

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MATLAB: How to use the Finite Difference Method to get the gradient

Here is an example of a function that uses gradest correctly:

function [F, g] = myfun(x)
fun = @(y) 2*sum(sin(y)) + 3;
F = fun(x);
g = gradest(fun,x);

The key differences are:

the name of the function fun is different from myfun
fun and its gradient are both evaluated at x.

Also, I have made it more efficient in a couple of other ways. Now you can test this directly using:

x = rand(4,1);
ganalytic = 2*cos(x)'; % This is the analytic gradient
[F,g] = myfun(x);
max(abs(g-ganalytic))

The last line tells you the maximum difference between the analytic and numerical gradients.

MATLAB: Minimization of two variables

Hello,

Here is an example for your problem, which you can refer

clear
xiyi = [0,1; 
        1,3;
       -1 2];
    
x0 = zeros(size(xiyi));
fun = @(x) max(sqrt((x(:,1)-xiyi(:,1)).^2 + (x(:,2)-xiyi(:,2)).^2))...
    - min(sqrt((x(:,1)-xiyi(:,1)).^2 + (x(:,2)-xiyi(:,2)).^2));
xsol = fminsearch(fun,x0)

It is assumed that xi and yi are the first and second column of vector xiyi (in the code).

The solution (x,y) will be stored in xsol.

Best Answer

Related Solutions

MATLAB: How to use the Finite Difference Method to get the gradient

MATLAB: Minimization of two variables

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