system of equations with nonlinear constraint

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Mohammadfarid ghasemi
评论： Torsten 2017-4-19
Hi, I have a system of three linear equations and three unknowns as below:
x(1).*(A11-B)+x(2).*A12+x(3).*A13=0
x(1).*A12 +x(2).*(A22-B)+x(3).*A23=0
x(1).*A13 +x(3).*(A33-B)+x(2).*A23=0
applying the fsolve yields the obvious answer of [0 0 0], Therefore, I have to define the following nonlinear and linear constraints:
x(1)^2+x(2)^2+x(3)^2=1.0 & -1<=x(1),x(2),x(3)<=1
I'm familiar with fmincon but it is applicable for scalar functions when one wants to find min f(x). I wonder how can I solve the aforementioned problem? Thank you so much for your time and attention.
  2 个评论
Torsten
Torsten 2017-4-19
A11,A12,A13,A22,A23,A33,B are given constants ?
Best wishes
Torsten.
Mohammadfarid ghasemi
Mohammadfarid ghasemi 2017-4-19
Yes, x is the 3*1 array of unknowns and the A11,A12,A13,A22,A23,A33,B are the known scalars.
Regards,
Farid

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Torsten
Torsten 2017-4-19
编辑：Torsten 2017-4-19
Then x is a normalized eigenvector to the minimum eigenvalue of the matrix
M=A*transpose(A)
where
A=[A11-B A12 A13;A12 A22-B A23;A13 A23 A33-B]
help eig
Best wishes
Torsten.
  3 个评论
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Torsten
Torsten 2017-4-19
Take a look at this thread:
https://de.mathworks.com/matlabcentral/answers/328754-rotation-that-maximises-a-vector-length
You search for a vector "that minimizes a vector length".
Best wishes
Torsten.

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