MATLAB: Maximize a system of nonlinear equation

equationmaximizenonlinearoptimizationsystem

Hi. I have a problem with the definition of a script. I have 2 functions of 3 variables. I need ( if it exists maybe with fmincon) a way to find the optimum valors for the three variables in order to maximize simultaniously the two equations. Thanks a lot

Best Answer

One approach:

f = @(x) norm([x(1).^2 + 2*x(2) + x(3); exp(x(1)).*sin(x(2)) + cos(x(3))]);
[X, fval] = fminunc(@(x)-f(x), rand(3,1));

Here ‘f’ has 2 equations in 3 unknowns. Use your own equations, and your own constraints with fmincon.

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MATLAB: How to do parameter fitting for a system of equations with 3 independent variables

xdata = horzcat(x1,x2,x3);
ydata = horzcat(y1,y2,y3);
fun=@(b,xdata) horzcat((b(1)+b(4))*x1./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(2)+b(5))*x2./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(3)+b(6))*x3./(1+b(1)*x1+b(2)*x2+b(3)*x3));
b0=[1 ; 1 ; 1 ; 1 ; 1 ; 1];
[x,resnorm] = lsqcurvefit(fun,b0,xdata,ydata);

Best wishes

Torsten.

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

You didn’t show your code, so I’m not certain what you’re doing.

You have to combine your independent variables in a matrix (I prefer column vectors for the independent and dependent variables), present them as one variable, then address the individual columns as the individual variables in your objective function.

For example:

x1x2x3 = [x1(:) x2(:) x3(:)];
y = y(:);
y = (k,x) k(1).*(1-exp(k(2).*x1x2x3(:,1))).*x1x2x3(:,3).^2 + ...

I’m not certain I parsed the parentheses correctly, so I’ll let you sort that.

Here, you would call nlinfit as:

k_est = nlinfit(x1x2x3, y, modelfun, k0);

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MATLAB: How to do parameter fitting for a system of equations with 3 independent variables

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

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