MATLAB: Quasi-Newton method for optimization

optimizationquasi newton methodquasi-newton

Given the set of 4 linear equations above, I'd like to optimize unknown parameters A, B, and C using a quasi-newton method. For example, coefficients r and given values R are as below:
Could you somebody help me with this?

Best Answer

Use FMINCON to minimize
norm(r*x-R)^2
with constraints
sum(x)=1
x>=0
r=[0.22 9.94 0.08;
   0.16 0.95 0.08;
   0.07 0.87 0.08];
R = [0.49; 0.42; 0.19]
x = fmincon(@(x) norm(r*x-R)^2, ones(3,1)/3, [], [], ones(1,3), 1, zeros(3,1), []);
A = x(1)
B = x(2)
C = x(3)
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